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Search: All articles in the CMB digital archive with keyword surface

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1. CMB Online first

Reichstein, Zinovy; Vistoli, Angelo
 On the dimension of the locus of determinantal hypersurfaces The characteristic polynomial $P_A(x_0, \dots, x_r)$ of an $r$-tuple $A := (A_1, \dots, A_r)$ of $n \times n$-matrices is defined as $P_A(x_0, \dots, x_r) := \det(x_0 I + x_1 A_1 + \dots + x_r A_r) \, .$ We show that if $r \geqslant 3$ and $A := (A_1, \dots, A_r)$ is an $r$-tuple of $n \times n$-matrices in general position, then up to conjugacy, there are only finitely many $r$-tuples $A' := (A_1', \dots, A_r')$ such that $p_A = p_{A'}$. Equivalently, the locus of determinantal hypersurfaces of degree $n$ in $\mathbf{P}^r$ is irreducible of dimension $(r-1)n^2 + 1$. Keywords:determinantal hypersurface, matrix invariant, $q$-binomial coefficientCategories:14M12, 15A22, 05A10

2. CMB 2016 (vol 59 pp. 776)

Gauthier, Paul M; Sharifi, Fatemeh
 The CarathÃ©odory Reflection Principle and Osgood-CarathÃ©odory Theorem on Riemann Surfaces The Osgood-CarathÃ©odory theorem asserts that conformal mappings between Jordan domains extend to homeomorphisms between their closures. For multiply-connected domains on Riemann surfaces, similar results can be reduced to the simply-connected case, but we find it simpler to deduce such results using a direct analogue of the CarathÃ©odory reflection principle. Keywords:bordered Riemann surface, reflection principle, Osgood-CarathÃ©odoryCategories:30C25, 30F99

3. CMB Online first

Gauthier, Paul M; Sharifi, Fatemeh
 Luzin-type holomorphic approximation on closed subsets of open Riemann surfaces It is known that if $E$ is a closed subset of an open Riemann surface $R$ and $f$ is a holomorphic function on a neighbourhood of $E,$ then it is usually" not possible to approximate $f$ uniformly by functions holomorphic on all of $R.$ We show, however, that for every open Riemann surface $R$ and every closed subset $E\subset R,$ there is closed subset $F\subset E,$ which approximates $E$ extremely well, such that every function holomorphic on $F$ can be approximated much better than uniformly by functions holomorphic on $R$. Keywords:Carleman approximation, tangential approximation, Myrberg surfaceCategories:30E15, 30F99

4. CMB 2016 (vol 59 pp. 813)

Kaimakamis, George; Panagiotidou, Konstantina; Pérez, Juan de Dios
 A Classification of Three-dimensional Real Hypersurfaces in Non-flat Complex Space Forms in Terms of Their generalized Tanaka-Webster Lie Derivative On a real hypersurface $M$ in a non-flat complex space form there exist the Levi-Civita and the k-th generalized Tanaka-Webster connections. The aim of the present paper is to study three dimensional real hypersurfaces in non-flat complex space forms, whose Lie derivative of the structure Jacobi operator with respect to the Levi-Civita connections coincides with the Lie derivative of it with respect to the k-th generalized Tanaka-Webster connection. The Lie derivatives are considered in direction of the structure vector field and in directions of any vecro field orthogonal to the structure vector field. Keywords:$k$-th generalized Tanaka-Webster connection, non-flat complex space form, real hypersurface, Lie derivative, structure Jacobi operatorCategories:53C15, 53B25

5. CMB Online first

Karzhemanov, Ilya
 On polarized K3 surfaces of genus 33 We prove that the moduli space of smooth primitively polarized $\mathrm{K3}$ surfaces of genus $33$ is unirational. Keywords:K3 surface, moduli space, unirationalityCategories:14J28, 14J15, 14M20

6. CMB 2016 (vol 59 pp. 721)

Pérez, Juan de Dios; Lee, Hyunjin; Suh, Young Jin; Woo, Changhwa
 Real Hypersurfaces in Complex Two-plane Grassmannians with Reeb Parallel Ricci Tensor in the GTW Connection There are several kinds of classification problems for real hypersurfaces in complex two-plane Grassmannians $G_2({\mathbb C}^{m+2})$. Among them, Suh classified Hopf hypersurfaces $M$ in $G_2({\mathbb C}^{m+2})$ with Reeb parallel Ricci tensor in Levi-Civita connection. In this paper, we introduce the notion of generalized Tanaka-Webster (in shortly, GTW) Reeb parallel Ricci tensor for Hopf hypersurface $M$ in $G_2({\mathbb C}^{m+2})$. Next, we give a complete classification of Hopf hypersurfaces in $G_2({\mathbb C}^{m+2})$ with GTW Reeb parallel Ricci tensor. Keywords:Complex two-plane Grassmannian, real hypersurface, Hopf hypersurface, generalized Tanaka-Webster connection, parallelism, Reeb parallelism, Ricci tensorCategories:53C40, 53C15

7. CMB 2015 (vol 58 pp. 673)

Achter, Jeffrey; Williams, Cassandra
 Local Heuristics and an Exact Formula for Abelian Surfaces Over Finite Fields Consider a quartic $q$-Weil polynomial $f$. Motivated by equidistribution considerations, we define, for each prime $\ell$, a local factor that measures the relative frequency with which $f\bmod \ell$ occurs as the characteristic polynomial of a symplectic similitude over $\mathbb{F}_\ell$. For a certain class of polynomials, we show that the resulting infinite product calculates the number of principally polarized abelian surfaces over $\mathbb{F}_q$ with Weil polynomial $f$. Keywords:abelian surfaces, finite fields, random matricesCategory:14K02

8. CMB 2015 (vol 58 pp. 835)

de Dios Pérez, Juan; Suh, Young Jin; Woo, Changhwa
 Real Hypersurfaces in Complex Two-Plane Grassmannians with GTW Harmonic Curvature We prove the non-existence of Hopf real hypersurfaces in complex two-plane Grassmannians with harmonic curvature with respect to the generalized Tanaka-Webster connection if they satisfy some further conditions. Keywords:real hypersurfaces, complex two-plane Grassmannians, Hopf hypersurface, generalized Tanaka-Webster connection, harmonic curvatureCategories:53C40, 53C15

9. CMB 2015 (vol 59 pp. 13)

 On classes $Q_p^\#$ for Hyperbolic Riemann surfaces The $Q_p$ spaces of holomorphic functions on the disk, hyperbolic Riemann surfaces or complex unit ball have been studied deeply. Meanwhile, there are a lot of papers devoted to the $Q^\#_p$ classes of meromorphic functions on the disk or hyperbolic Riemann surfaces. In this paper, we prove the nesting property (inclusion relations) of $Q^\#_p$ classes on hyperbolic Riemann surfaces. The same property for $Q_p$ spaces was also established systematically and precisely in earlier work by the authors of this paper. Keywords:$Q_p^\#$ class, hyperbolic Riemann surface, spherical Dirichlet function,Categories:30D50, 30F35

10. CMB 2015 (vol 58 pp. 285)

Karpukhin, Mikhail
 Spectral Properties of a Family of Minimal Tori of Revolution in Five-dimensional Sphere The normalized eigenvalues $\Lambda_i(M,g)$ of the Laplace-Beltrami operator can be considered as functionals on the space of all Riemannian metrics $g$ on a fixed surface $M$. In recent papers several explicit examples of extremal metrics were provided. These metrics are induced by minimal immersions of surfaces in $\mathbb{S}^3$ or $\mathbb{S}^4$. In the present paper a family of extremal metrics induced by minimal immersions in $\mathbb{S}^5$ is investigated. Keywords:extremal metric, minimal surfaceCategory:58J50

11. CMB 2014 (vol 58 pp. 196)

Yang, Qingjie; Zhong, Weiting
 Dihedral Groups of order $2p$ of Automorphisms of Compact Riemann Surfaces of Genus $p-1$ In this paper we prove that there is only one conjugacy class of dihedral group of order $2p$ in the $2(p-1)\times 2(p-1)$ integral symplectic group can be realized by an analytic automorphism group of compact connected Riemann surfaces of genus $p-1$. A pair of representative generators of the realizable class is also given. Keywords:dihedral group, automorphism group, Riemann surface, integral symplectic matrix, fundamental domainCategories:20H25, 57M60

12. CMB 2014 (vol 57 pp. 765)

da Silva, Rosângela Maria; Tenenblat, Keti
 Helicoidal Minimal Surfaces in a Finsler Space of Randers Type We consider the Finsler space $(\bar{M}^3, \bar{F})$ obtained by perturbing the Euclidean metric of $\mathbb{R}^3$ by a rotation. It is the open region of $\mathbb{R}^3$ bounded by a cylinder with a Randers metric. Using the Busemann-Hausdorff volume form, we obtain the differential equation that characterizes the helicoidal minimal surfaces in $\bar{M}^3$. We prove that the helicoid is a minimal surface in $\bar{M}^3$, only if the axis of the helicoid is the axis of the cylinder. Moreover, we prove that, in the Randers space $(\bar{M}^3, \bar{F})$, the only minimal surfaces in the Bonnet family, with fixed axis $O\bar{x}^3$, are the catenoids and the helicoids. Keywords:minimal surfaces, helicoidal surfaces, Finsler space, Randers spaceCategories:53A10, 53B40

13. CMB 2013 (vol 57 pp. 870)

Parlier, Hugo
 A Short Note on Short Pants It is a theorem of Bers that any closed hyperbolic surface admits a pants decomposition consisting of curves of bounded length where the bound only depends on the topology of the surface. The question of the quantification of the optimal constants has been well studied and the best upper bounds to date are linear in genus, a theorem of Buser and SeppÃ¤lÃ¤. The goal of this note is to give a short proof of a linear upper bound which slightly improve the best known bound. Keywords:hyperbolic surfaces, geodesics, pants decompositionsCategories:30F10, 32G15, 53C22

14. CMB 2013 (vol 57 pp. 821)

Jeong, Imsoon; Kim, Seonhui; Suh, Young Jin
 Real Hypersurfaces in Complex Two-Plane Grassmannians with Reeb Parallel Structure Jacobi Operator In this paper we give a characterization of a real hypersurface of Type~$(A)$ in complex two-plane Grassmannians ${ { {G_2({\mathbb C}^{m+2})} } }$, which means a tube over a totally geodesic $G_{2}(\mathbb C^{m+1})$ in ${G_2({\mathbb C}^{m+2})}$, by the Reeb parallel structure Jacobi operator ${\nabla}_{\xi}R_{\xi}=0$. Keywords:real hypersurfaces, complex two-plane Grassmannians, Hopf hypersurface, Reeb parallel, structure Jacobi operatorCategories:53C40, 53C15

15. CMB 2012 (vol 56 pp. 466)

 Inclusion Relations for New Function Spaces on Riemann Surfaces We introduce and study some new function spaces on Riemann surfaces. For certain parameter values these spaces coincide with the classical Dirichlet space, BMOA or the recently defined $Q_p$ space. We establish inclusion relations that generalize earlier known inclusions between the above-mentioned spaces. Keywords:Bloch space, BMOA, $Q_p$, Green's function, hyperbolic Riemann surfaceCategories:30F35, 30H25, 30H30

16. CMB 2011 (vol 56 pp. 306)

Pérez, Juan de Dios; Suh, Young Jin
 Real Hypersurfaces in Complex Projective Space Whose Structure Jacobi Operator is Lie $\mathbb{D}$-parallel We prove the non-existence of real hypersurfaces in complex projective space whose structure Jacobi operator is Lie $\mathbb{D}$-parallel and satisfies a further condition. Keywords:complex projective space, real hypersurface, structure Jacobi operatorCategories:53C15, 53C40

17. CMB 2011 (vol 56 pp. 500)

Browning, T. D.
 The Lang--Weil Estimate for Cubic Hypersurfaces An improved estimate is provided for the number of $\mathbb{F}_q$-rational points on a geometrically irreducible, projective, cubic hypersurface that is not equal to a cone. Keywords:cubic hypersurface, rational points, finite fieldsCategories:11G25, 14G15

18. CMB 2011 (vol 55 pp. 26)

Bertin, Marie José
 A Mahler Measure of a $K3$ Surface Expressed as a Dirichlet $L$-Series We present another example of a $3$-variable polynomial defining a $K3$-hypersurface and having a logarithmic Mahler measure expressed in terms of a Dirichlet $L$-series. Keywords:modular Mahler measure, Eisenstein-Kronecker series, $L$-series of $K3$-surfaces, $l$-adic representations, LivnÃ© criterion, Rankin-Cohen bracketsCategories:11, 14D, 14J

19. CMB 2011 (vol 55 pp. 176)

Spirn, Daniel; Wright, J. Douglas
 Linear Dispersive Decay Estimates for the 3+1 Dimensional Water Wave Equation with Surface Tension We consider the linearization of the three-dimensional water waves equation with surface tension about a flat interface. Using oscillatory integral methods, we prove that solutions of this equation demonstrate dispersive decay at the somewhat surprising rate of $t^{-5/6}$. This rate is due to competition between surface tension and gravitation at $O(1)$ wave numbers and is connected to the fact that, in the presence of surface tension, there is a so-called "slowest wave". Additionally, we combine our dispersive estimates with $L^2$ type energy bounds to prove a family of Strichartz estimates. Keywords:oscillatory integrals, water waves, surface tension, Strichartz estimatesCategories:76B07, 76B15, 76B45

20. CMB 2011 (vol 55 pp. 114)

Kon, S. H.; Loo, Tee-How
 On Characterizations of Real Hypersurfaces in a Complex Space Form with $\eta$-Parallel Shape Operator In this paper we study real hypersurfaces in a non-flat complex space form with $\eta$-parallel shape operator. Several partial characterizations of these real hypersurfaces are obtained. Keywords:complex space form, Hopf hypersurfaces, ruled real hypersurfaces, $\eta$-parallel shape operatorCategories:53C40, 53C15

21. CMB 2011 (vol 54 pp. 422)

Pérez, Juan de Dios; Suh, Young Jin
 Two Conditions on the Structure Jacobi Operator for Real Hypersurfaces in Complex Projective Space We classify real hypersurfaces in complex projective space whose structure Jacobi operator satisfies two conditions at the same time. Keywords:complex projective space, real hypersurface, structure Jacobi operator, two conditionsCategories:53C15, 53B25

22. CMB 2011 (vol 54 pp. 311)

Marzougui, Habib
 Some Remarks Concerning the Topological Characterization of Limit Sets for Surface Flows We give some extension to theorems of JimÃ©nez LÃ³pez and Soler LÃ³pez concerning the topological characterization for limit sets of continuous flows on closed orientable surfaces. Keywords:flows on surfaces, orbits, class of an orbit, singularities, minimal set, limit set, regular cylinder Categories:37B20, 37E35

23. CMB 2009 (vol 53 pp. 218)

Biswas, Indranil
 Restriction of the Tangent Bundle of $G/P$ to a Hypersurface Let P be a maximal proper parabolic subgroup of a connected simple linear algebraic group G, defined over $\mathbb C$, such that $n := \dim_{\mathbb C} G/P \geq 4$. Let $\iota \colon Z \hookrightarrow G/P$ be a reduced smooth hypersurface of degree at least $(n-1)\cdot \operatorname{degree}(T(G/P))/n$. We prove that the restriction of the tangent bundle $\iota^*TG/P$ is semistable. Keywords:tangent bundle, homogeneous space, semistability, hypersurfaceCategories:14F05, 14J60, 14M15

24. CMB 2009 (vol 52 pp. 493)

Artebani, Michela
 A One-Dimensional Family of $K3$ Surfaces with a $\Z_4$ Action The minimal resolution of the degree four cyclic cover of the plane branched along a GIT stable quartic is a $K3$ surface with a non symplectic action of $\Z_4$. In this paper we study the geometry of the one-dimensional family of $K3$ surfaces associated to the locus of plane quartics with five nodes. Keywords:genus three curves, $K3$ surfacesCategories:14J28, 14J50, 14J10

25. CMB 2009 (vol 52 pp. 257)

Ikeda, Toru
 Essential Surfaces in Graph Link Exteriors An irreducible graph manifold $M$ contains an essential torus if it is not a special Seifert manifold. Whether $M$ contains a closed essential surface of negative Euler characteristic or not depends on the difference of Seifert fibrations from the two sides of a torus system which splits $M$ into Seifert manifolds. However, it is not easy to characterize geometrically the class of irreducible graph manifolds which contain such surfaces. This article studies this problem in the case of graph link exteriors. Keywords:Graph link, Graph manifold, Seifert manifold, Essential surfaceCategory:57M25
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