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

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1. CMB Online first

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

2. CMB 2012 (vol 56 pp. 640)

Türkmen, İnan Utku
 Regulator Indecomposable Cycles on a Product of Elliptic Curves We provide a novel proof of the existence of regulator indecomposables in the cycle group $CH^2(X,1)$, where $X$ is a sufficiently general product of two elliptic curves. In particular, the nature of our proof provides an illustration of Beilinson rigidity. Keywords:real regulator, regulator indecomposable, higher Chow group, indecomposable cycleCategory:14C25

3. 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

4. CMB 2011 (vol 55 pp. 752)

Hickel, M.; Rond, G.
 Approximation of Holomorphic Solutions of a System of Real Analytic Equations We prove the existence of an approximation function for holomorphic solutions of a system of real analytic equations. For this we use ultraproducts and Weierstrass systems introduced by J. Denef and L. Lipshitz. We also prove a version of the PÅoski smoothing theorem in this case. Keywords:Artin approximation, real analytic equationsCategories:13B40, 13L05, 14F12

5. CMB 2011 (vol 55 pp. 611)

 Chen Inequalities for Submanifolds of Real Space Forms with a Semi-Symmetric Non-Metric Connection In this paper we prove Chen inequalities for submanifolds of real space forms endowed with a semi-symmetric non-metric connection, i.e., relations between the mean curvature associated with a semi-symmetric non-metric connection, scalar and sectional curvatures, Ricci curvatures and the sectional curvature of the ambient space. The equality cases are considered. Keywords:real space form, semi-symmetric non-metric connection, Ricci curvatureCategories:53C40, 53B05, 53B15

6. 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

7. 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

8. CMB 2011 (vol 54 pp. 593)

Boersema, Jeffrey L.; Ruiz, Efren
 Stability of Real $C^*$-Algebras We will give a characterization of stable real $C^*$-algebras analogous to the one given for complex $C^*$-algebras by Hjelmborg and RÃ¸rdam. Using this result, we will prove that any real $C^*$-algebra satisfying the corona factorization property is stable if and only if its complexification is stable. Real $C^*$-algebras satisfying the corona factorization property include AF-algebras and purely infinite $C^*$-algebras. We will also provide an example of a simple unstable $C^*$-algebra, the complexification of which is stable. Keywords:stability, real C*-algebrasCategory:46L05

9. CMB 2009 (vol 53 pp. 51)

Cobos, Fernando; Fernández-Cabrera, Luz M.
 On the Relationship Between Interpolation of Banach Algebras and Interpolation of Bilinear Operators We show that if the general real method $(\cdot ,\cdot )_\Gamma$ preserves the Banach-algebra structure, then a bilinear interpolation theorem holds for $(\cdot ,\cdot )_\Gamma$. Keywords:real interpolation, bilinear operators, Banach algebrasCategories:46B70, 46M35, 46H05

10. CMB 2009 (vol 52 pp. 39)

Cimpri\v{c}, Jakob
 A Representation Theorem for Archimedean Quadratic Modules on $*$-Rings We present a new approach to noncommutative real algebraic geometry based on the representation theory of $C^\ast$-algebras. An important result in commutative real algebraic geometry is Jacobi's representation theorem for archimedean quadratic modules on commutative rings. We show that this theorem is a consequence of the Gelfand--Naimark representation theorem for commutative $C^\ast$-algebras. A noncommutative version of Gelfand--Naimark theory was studied by I. Fujimoto. We use his results to generalize Jacobi's theorem to associative rings with involution. Keywords:Ordered rings with involution, $C^\ast$-algebras and their representations, noncommutative convexity theory, real algebraic geometryCategories:16W80, 46L05, 46L89, 14P99

11. CMB 2008 (vol 51 pp. 359)

Cho, Jong Taek; Ki, U-Hang
 Real Hypersurfaces in Complex Space Forms with Reeb Flow Symmetric Structure Jacobi Operator Real hypersurfaces in a complex space form whose structure Jacobi operator is symmetric along the Reeb flow are studied. Among them, homogeneous real hypersurfaces of type $(A)$ in a complex projective or hyperbolic space are characterized as those whose structure Jacobi operator commutes with the shape operator. Keywords:complex space form, real hypersurface, structure Jacobi operatorCategories:53B20, 53C15, 53C25

12. CMB 2005 (vol 48 pp. 561)

Foth, Philip
 A Note on Lagrangian Loci of Quotients We study Hamiltonian actions of compact groups in the presence of compatible involutions. We show that the Lagrangian fixed point set on the symplectically reduced space is isomorphic to the disjoint union of the involutively reduced spaces corresponding to involutions on the group strongly inner to the given one. Our techniques imply that the solution to the eigenvalues of a sum problem for a given real form can be reduced to the quasi-split real form in the same inner class. We also consider invariant quotients with respect to the corresponding real form of the complexified group. Keywords:Quotients, involutions, real forms, Lagrangian lociCategory:53D20

13. CMB 2005 (vol 48 pp. 121)

Mollin, R. A.
 Necessary and Sufficient Conditions for the Central Norm to Equal $2^h$ in the Simple Continued Fraction Expansion of $\sqrt{2^hc}$ for Any Odd $c>1$ We look at the simple continued fraction expansion of $\sqrt{D}$ for any $D=2^hc$ where $c>1$ is odd with a goal of determining necessary and sufficient conditions for the central norm (as determined by the infrastructure of the underlying real quadratic order therein) to be $2^h$. At the end of the paper, we also address the case where $D=c$ is odd and the central norm of $\sqrt{D}$ is equal to $2$. Keywords:quadratic Diophantine equations, simple continued fractions,, norms of ideals, infrastructure of real quadratic fieldsCategories:11A55, 11D09, 11R11

14. CMB 1999 (vol 42 pp. 274)

Dădărlat, Marius; Eilers, Søren
 The Bockstein Map is Necessary We construct two non-isomorphic nuclear, stably finite, real rank zero $C^\ast$-algebras $E$ and $E'$ for which there is an isomorphism of ordered groups $\Theta\colon \bigoplus_{n \ge 0} K_\bullet(E;\ZZ/n) \to \bigoplus_{n \ge 0} K_\bullet(E';\ZZ/n)$ which is compatible with all the coefficient transformations. The $C^\ast$-algebras $E$ and $E'$ are not isomorphic since there is no $\Theta$ as above which is also compatible with the Bockstein operations. By tensoring with Cuntz's algebra $\OO_\infty$ one obtains a pair of non-isomorphic, real rank zero, purely infinite $C^\ast$-algebras with similar properties. Keywords:$K$-theory, torsion coefficients, natural transformations, Bockstein maps, $C^\ast$-algebras, real rank zero, purely infinite, classificationCategories:46L35, 46L80, 19K14