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

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1. CMB Online first

Brendle, Simon; Chodosh, Otis
On the maximum curvature of closed curves in negatively curved manifolds
Motivated by Almgren's work on the isoperimetric inequality, we prove a sharp inequality relating the length and maximum curvature of a closed curve in a complete, simply connected manifold of sectional curvature at most $-1$. Moreover, if equality holds, then the norm of the geodesic curvature is constant and the torsion vanishes. The proof involves an application of the maximum principle to a function defined on pairs of points.

Keywords:manifold, curvature

2. CMB 2014 (vol 57 pp. 673)

Ahmadi, S. Ruhallah; Gilligan, Bruce
Complexifying Lie Group Actions on Homogeneous Manifolds of Non-compact Dimension Two
If $X$ is a connected complex manifold with $d_X = 2$ that admits a (connected) Lie group $G$ acting transitively as a group of holomorphic transformations, then the action extends to an action of the complexification $\widehat{G}$ of $G$ on $X$ except when either the unit disk in the complex plane or a strictly pseudoconcave homogeneous complex manifold is the base or fiber of some homogeneous fibration of $X$.

Keywords:homogeneous complex manifold, non-compact dimension two, complexification

3. CMB 2013 (vol 57 pp. 526)

Heil, Wolfgang; Wang, Dongxu
On $3$-manifolds with Torus or Klein Bottle Category Two
A subset $W$ of a closed manifold $M$ is $K$-contractible, where $K$ is a torus or Kleinbottle, if the inclusion $W\rightarrow M$ factors homotopically through a map to $K$. The image of $\pi_1 (W)$ (for any base point) is a subgroup of $\pi_1 (M)$ that is isomorphic to a subgroup of a quotient group of $\pi_1 (K)$. Subsets of $M$ with this latter property are called $\mathcal{G}_K$-contractible. We obtain a list of the closed $3$-manifolds that can be covered by two open $\mathcal{G}_K$-contractible subsets. This is applied to obtain a list of the possible closed prime $3$-manifolds that can be covered by two open $K$-contractible subsets.

Keywords:Lusternik--Schnirelmann category, coverings of $3$-manifolds by open $K$-contractible sets
Categories:57N10, 55M30, 57M27, 57N16

4. CMB 2013 (vol 57 pp. 401)

Perrone, Domenico
Curvature of $K$-contact Semi-Riemannian Manifolds
In this paper we characterize $K$-contact semi-Riemannian manifolds and Sasakian semi-Riemannian manifolds in terms of curvature. Moreover, we show that any conformally flat $K$-contact semi-Riemannian manifold is Sasakian and of constant sectional curvature $\kappa=\varepsilon$, where $\varepsilon =\pm 1$ denotes the causal character of the Reeb vector field. Finally, we give some results about the curvature of a $K$-contact Lorentzian manifold.

Keywords:contact semi-Riemannian structures, $K$-contact structures, conformally flat manifolds, Einstein Lorentzian-Sasaki manifolds
Categories:53C50, 53C25, 53B30

5. CMB 2013 (vol 57 pp. 357)

Lauret, Emilio A.
Representation Equivalent Bieberbach Groups and Strongly Isospectral Flat Manifolds
Let $\Gamma_1$ and $\Gamma_2$ be Bieberbach groups contained in the full isometry group $G$ of $\mathbb{R}^n$. We prove that if the compact flat manifolds $\Gamma_1\backslash\mathbb{R}^n$ and $\Gamma_2\backslash\mathbb{R}^n$ are strongly isospectral then the Bieberbach groups $\Gamma_1$ and $\Gamma_2$ are representation equivalent, that is, the right regular representations $L^2(\Gamma_1\backslash G)$ and $L^2(\Gamma_2\backslash G)$ are unitarily equivalent.

Keywords:representation equivalent, strongly isospectrality, compact flat manifolds
Categories:58J53, 22D10

6. CMB 2013 (vol 57 pp. 335)

Karassev, A.; Todorov, V.; Valov, V.
Alexandroff Manifolds and Homogeneous Continua
ny homogeneous, metric $ANR$-continuum is a $V^n_G$-continuum provided $\dim_GX=n\geq 1$ and $\check{H}^n(X;G)\neq 0$, where $G$ is a principal ideal domain. This implies that any homogeneous $n$-dimensional metric $ANR$-continuum is a $V^n$-continuum in the sense of Alexandroff. We also prove that any finite-dimensional homogeneous metric continuum $X$, satisfying $\check{H}^n(X;G)\neq 0$ for some group $G$ and $n\geq 1$, cannot be separated by a compactum $K$ with $\check{H}^{n-1}(K;G)=0$ and $\dim_G K\leq n-1$. This provides a partial answer to a question of Kallipoliti-Papasoglu whether any two-dimensional homogeneous Peano continuum cannot be separated by arcs.

Keywords:Cantor manifold, cohomological dimension, cohomology groups, homogeneous compactum, separator, $V^n$-continuum
Categories:54F45, 54F15

7. CMB 2012 (vol 57 pp. 209)

Zhao, Wei
Erratum to the Paper "A Lower Bound for the Length of Closed Geodesics on a Finsler Manifold"
We correct two clerical errors made in the paper "A Lower Bound for the Length of Closed Geodesics on a Finsler Manifold".

Keywords:Finsler manifold, closed geodesic, injective radius
Categories:53B40, 53C22

8. CMB 2012 (vol 57 pp. 240)

Bernardes, Nilson C.
Addendum to ``Limit Sets of Typical Homeomorphisms''
Given an integer $n \geq 3$, a metrizable compact topological $n$-manifold $X$ with boundary, and a finite positive Borel measure $\mu$ on $X$, we prove that for the typical homeomorphism $f : X \to X$, it is true that for $\mu$-almost every point $x$ in $X$ the restriction of $f$ (respectively of $f^{-1}$) to the omega limit set $\omega(f,x)$ (respectively to the alpha limit set $\alpha(f,x)$) is topologically conjugate to the universal odometer.

Keywords:topological manifolds, homeomorphisms, measures, Baire category, limit sets
Categories:37B20, 54H20, 28C15, 54C35, 54E52

9. CMB 2012 (vol 57 pp. 194)

Zhao, Wei
A Lower Bound for the Length of Closed Geodesics on a Finsler Manifold
In this paper, we obtain a lower bound for the length of closed geodesics on an arbitrary closed Finsler manifold.

Keywords:Finsler manifold, closed geodesic, injective radius
Categories:53B40, 53C22

10. CMB 2012 (vol 57 pp. 12)

Aribi, Amine; Dragomir, Sorin; El Soufi, Ahmad
On the Continuity of the Eigenvalues of a Sublaplacian
We study the behavior of the eigenvalues of a sublaplacian $\Delta_b$ on a compact strictly pseudoconvex CR manifold $M$, as functions on the set ${\mathcal P}_+$ of positively oriented contact forms on $M$ by endowing ${\mathcal P}_+$ with a natural metric topology.

Keywords:CR manifold, contact form, sublaplacian, Fefferman metric
Categories:32V20, 53C56

11. CMB 2011 (vol 56 pp. 173)

Sahin, Bayram
Semi-invariant Submersions from Almost Hermitian Manifolds
We introduce semi-invariant Riemannian submersions from almost Hermitian manifolds onto Riemannian manifolds. We give examples, investigate the geometry of foliations that arise from the definition of a Riemannian submersion, and find necessary sufficient conditions for total manifold to be a locally product Riemannian manifold. We also find necessary and sufficient conditions for a semi-invariant submersion to be totally geodesic. Moreover, we obtain a classification for semi-invariant submersions with totally umbilical fibers and show that such submersions put some restrictions on total manifolds.

Keywords:Riemannian submersion, Hermitian manifold, anti-invariant Riemannian submersion, semi-invariant submersion
Categories:53B20, 53C43

12. CMB 2011 (vol 55 pp. 632)

Pigola, S.; Rimoldi, M.
Characterizations of Model Manifolds by Means of Certain Differential Systems
We prove metric rigidity for complete manifolds supporting solutions of certain second order differential systems, thus extending classical works on a characterization of space-forms. Along the way, we also discover new characterizations of space-forms. We next generalize results concerning metric rigidity via equations involving vector fields.

Keywords:metric rigidity, model manifolds, Obata's type theorems

13. CMB 2011 (vol 55 pp. 225)

Bernardes, Nilson C.
Limit Sets of Typical Homeomorphisms
Given an integer $n \geq 3$, a metrizable compact topological $n$-manifold $X$ with boundary, and a finite positive Borel measure $\mu$ on $X$, we prove that for the typical homeomorphism $f \colon X \to X$, it is true that for $\mu$-almost every point $x$ in $X$ the limit set $\omega(f,x)$ is a Cantor set of Hausdorff dimension zero, each point of $\omega(f,x)$ has a dense orbit in $\omega(f,x)$, $f$ is non-sensitive at each point of $\omega(f,x)$, and the function $a \to \omega(f,a)$ is continuous at $x$.

Keywords:topological manifolds, homeomorphisms, measures, Baire category, limit sets
Categories:37B20, 54H20, 28C15, 54C35, 54E52

14. CMB 2011 (vol 55 pp. 164)

Pergher, Pedro L. Q.
Involutions Fixing $F^n \cup \{\text{Indecomposable}\}$
Let $M^m$ be an $m$-dimensional, closed and smooth manifold, equipped with a smooth involution $T\colon M^m \to M^m$ whose fixed point set has the form $F^n \cup F^j$, where $F^n$ and $F^j$ are submanifolds with dimensions $n$ and $j$, $F^j$ is indecomposable and $ n >j$. Write $n-j=2^pq$, where $q \ge 1$ is odd and $p \geq 0$, and set $m(n-j) = 2n+p-q+1$ if $p \leq q + 1$ and $m(n-j)= 2n + 2^{p-q}$ if $p \geq q$. In this paper we show that $m \le m(n-j) + 2j+1$. Further, we show that this bound is \emph{almost} best possible, by exhibiting examples $(M^{m(n-j) +2j},T)$ where the fixed point set of $T$ has the form $F^n \cup F^j$ described above, for every $2 \le j
Keywords:involution, projective space bundle, indecomposable manifold, splitting principle, Stiefel-Whitney class, characteristic number

15. CMB 2011 (vol 54 pp. 396)

Cho, Jong Taek; Inoguchi, Jun-ichi; Lee, Ji-Eun
Parabolic Geodesics in Sasakian $3$-Manifolds
We give explicit parametrizations for all parabolic geodesics in 3-dimensional Sasakian space forms.

Keywords:parabolic geodesics, pseudo-Hermitian geometry, Sasakian manifolds

16. CMB 2011 (vol 54 pp. 716)

Okassa, Eugène
Symplectic Lie-Rinehart-Jacobi Algebras and Contact Manifolds
We give a characterization of contact manifolds in terms of symplectic Lie-Rinehart-Jacobi algebras. We also give a sufficient condition for a Jacobi manifold to be a contact manifold.

Keywords:Lie-Rinehart algebras, differential operators, Jacobi manifolds, symplectic manifolds, contact manifolds
Categories:13N05, 53D05, 53D10

17. CMB 2010 (vol 53 pp. 674)

Kristály, Alexandru; Papageorgiou, Nikolaos S.; Varga, Csaba
Multiple Solutions for a Class of Neumann Elliptic Problems on Compact Riemannian Manifolds with Boundary
We study a semilinear elliptic problem on a compact Riemannian manifold with boundary, subject to an inhomogeneous Neumann boundary condition. Under various hypotheses on the nonlinear terms, depending on their behaviour in the origin and infinity, we prove multiplicity of solutions by using variational arguments.

Keywords:Riemannian manifold with boundary, Neumann problem, sublinearity at infinity, multiple solutions
Categories:58J05, 35P30

18. CMB 2010 (vol 53 pp. 684)

Proctor, Emily; Stanhope, Elizabeth
An Isospectral Deformation on an Infranil-Orbifold
We construct a Laplace isospectral deformation of metrics on an orbifold quotient of a nilmanifold. Each orbifold in the deformation contains singular points with order two isotropy. Isospectrality is obtained by modifying a generalization of Sunada's theorem due to DeTurck and Gordon.

Keywords:spectral geometry, global Riemannian geometry, orbifold, nilmanifold
Categories:58J53, 53C20

19. CMB 2010 (vol 53 pp. 564)

Watanabe, Yoshiyuki; Suh, Young Jin
On $6$-Dimensional Nearly Kähler Manifolds
In this paper we give a sufficient condition for a complete, simply connected, and strict nearly Kähler manifold of dimension 6 to be a homogeneous nearly Kähler manifold. This result was announced in a previous paper by the first author.

Keywords:Nearly Kähler manifold, 6-dimension, Homogeneous, The 1st Chern Class, Einstein manifolds
Categories:53C40, 53C15

20. CMB 2010 (vol 53 pp. 438)

Chigogidze, A.; Nagórko, A.
Near-Homeomorphisms of Nöbeling Manifolds
We characterize maps between $n$-dimensional Nöbeling manifolds that can be approximated by homeomorphisms.

Keywords:n-dimensional Nöbeling manifold, Z-set unknotting, near-homeomorphism
Categories:55M10, 54F45

21. CMB 2010 (vol 53 pp. 412)

Calvaruso, G.
Einstein-Like Lorentz Metrics and Three-Dimensional Curvature Homogeneity of Order One
We completely classify three-dimensional Lorentz manifolds, curvature homogeneous up to order one, equipped with Einstein-like metrics. New examples arise with respect to both homogeneous examples and three-dimensional Lorentz manifolds admitting a degenerate parallel null line field.

Keywords:Lorentz manifolds, curvature homogeneity, Einstein-like metrics
Categories:53C50, 53C20, 53C30

22. CMB 2009 (vol 53 pp. 122)

Mo, Xiaohuan; Zhou, Linfeng
A Class of Finsler Metrics with Bounded Cartan Torsion
In this paper, we find a class of $(\alpha,\beta)$ metrics which have a bounded Cartan torsion. This class contains all Randers metrics. Furthermore, we give some applications and obtain two corollaries about curvature of this metrics.

Keywords:Finsler manifold, $(\alpha,\beta)$ metric, Cartan torsion, R-quadratic, flag curvature

23. CMB 2009 (vol 53 pp. 206)

Atçeken, Mehmet
Semi-Slant Submanifolds of an Almost Paracontact Metric Manifold
In this paper, we define and study the geometry of semi-slant submanifolds of an almost paracontact metric manifold. We give some characterizations for a submanifold to be semi-slant submanifold to be semi-slant product and obtain integrability conditions for the distributions involved in the definition of a semi-slant submanifold.

Keywords:paracontact metric manifold, slant distribution, semi-slant submanifold, semi-slant product
Categories:53C15, 53C25, 53C40

24. 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 surface

25. CMB 2009 (vol 52 pp. 18)

Chinea, Domingo
Harmonicity of Holomorphic Maps Between Almost Hermitian Manifolds
In this paper we study holomorphic maps between almost Hermitian manifolds. We obtain a new criterion for the harmonicity of such holomorphic maps, and we deduce some applications to horizontally conformal holomorphic submersions.

Keywords:almost Hermitian manifolds, harmonic maps, harmonic morphism
Categories:53C15, 58E20
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