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8 results on '"Almost hypercomplex manifold"'

2. Quaternionic Kähler manifolds with Hermitian and Norden metrics.

Author

Manev, Mancho

Subjects
*QUATERNIONS, *KAHLERIAN manifolds, *HERMITIAN structures, *HYPERCOMPLEX numbers, *DIOPHANTINE equations, *EINSTEIN manifolds, *DIMENSIONS
Abstract

Almost hypercomplex manifolds with Hermitian and Norden metrics and more specially the corresponding quaternionic Kähler manifolds are considered. Some necessary and sufficient conditions for the investigated manifolds to be isotropic hyper-Kählerian and flat are found. It is proved that the quaternionic Kähler manifolds with the considered metric structure are Einstein for dimension at least 8. The class of the non-hyper-Kähler quaternionic Kähler manifolds of the considered type is determined. [ABSTRACT FROM AUTHOR]

Published
2012
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3. A CONNECTION WITH PARALLEL TOTALLY SKEW-SYMMETRIC TORSION ON A CLASS OF ALMOST HYPERCOMPLEX MANIFOLDS WITH HERMITIAN AND ANTI-HERMITIAN METRICS.

Author

MANEV, MANCHO and GRIBACHEV, KOSTADIN

Subjects
*TORSION, *ELASTIC solids, *STRAINS & stresses (Mechanics), *DEFORMATIONS (Mechanics), *MATHEMATICAL programming, *HERMITIAN structures, *MANIFOLDS (Mathematics)
Abstract

The subject of investigations are the almost hypercomplex manifolds with Hermitian and anti-Hermitian (Norden) metrics. A linear connection D is introduced such that the structure of these manifolds is parallel with respect to D and its torsion is totally skew-symmetric. The class of the nearly Kähler manifolds with respect to the first almost complex structure is of special interest. It is proved that D has a D-parallel torsion and is weak if it is not flat. Some curvature properties of these manifolds are studied. [ABSTRACT FROM AUTHOR]

Published
2011
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4. A connection with parallel torsion on almost hypercomplex manifolds with Hermitian and anti-Hermitian metrics

Author

Manev, Mancho

Subjects
*RIEMANNIAN manifolds, *HERMITIAN structures, *METRIC spaces, *TORSION, *CONFORMAL mapping, *MATHEMATICAL constants
Abstract

Abstract: Almost hypercomplex manifolds with Hermitian and anti-Hermitian metrics are considered. A linear connection is introduced such that the structure of these manifolds is parallel with respect to . Of special interest is the class of the locally conformally equivalent manifolds of the manifolds with covariantly constant almost complex structures and the case when the torsion of is -parallel. Curvature properties of these manifolds are studied. An example of 4-dimensional manifolds in the considered basic class is constructed and characterized. [ABSTRACT FROM AUTHOR]

Published
2011
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5. Almost hypercomplex pseudo-Hermitian manifolds and a 4-dimensional Lie group with such structure.

Author

Gribachev, Kostadin and Manev, Mancho

Subjects
*MANIFOLDS (Mathematics), *DIFFERENTIAL geometry, *HYPERBOLIC spaces, *LIE groups, *SYMMETRIC spaces
Abstract

Almost hypercomplex pseudo-Hermitian manifolds are considered. Isotropic hyper-Kähler manifolds are introduced. A 4-parametric family of 4-dimensional manifolds of this type is constructed on a Lie group. This family is characterized geometrically. The condition a 4-manifold to be isotropic hyper-Kähler is given. [ABSTRACT FROM AUTHOR]

Published
2008
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6. Natural Connections with Totally Skew-Symmetric Torsion on Manifolds with Norden-Type Metrics

Author

Manev, Mancho, Mekerov, Dimitar, and Gribachev, Kostadin

Subjects
Almost Contact Manifold, Norden Metric, Almost Complex Manifold, Almost Hypercomplex Manifold, B-metric, Mathematics::Differential Geometry, HKT-Connection, KT-Connection, Mathematics::Geometric Topology, Mathematics::Symplectic Geometry, Skew-Symmetric Torsion, Bismut Connection, Anti-Hermitian Metric
Abstract

This paper is a survey of results obtained by the authors on the geometry of connections with totally skew-symmetric torsion on the following manifolds: almost complex manifolds with Norden metric, almost contact manifolds with B-metric and almost hypercomplex manifolds with Hermitian and anti-Hermitian metric.

Published
2010

7. Espaces twistoriels et structures complexes non standards

Author

Guillaume Deschamps, Institut Élie Cartan de Nancy (IECN), Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS), and Deschamps, Guillaume

Subjects
Pure mathematics, métrique anti-autoduale, Spin structure, General Mathematics, structure spin, Fundamental theorem of Riemannian geometry, Twistor space, 01 natural sciences, parallelisable complex surface, Twistor theory, High Energy Physics::Theory, self-dual metric, almost hypercomplex manifold, Almost hypercomplex manifold, classification de Kodaira, 0103 physical sciences, 51M99, Hermitian manifold, 0101 mathematics, Mathematics, Enriques-Kodaira classification, 010102 general mathematics, Mathematical analysis, [MATH.MATH-CV]Mathematics [math]/Complex Variables [math.CV], Surface (topology), Fubini–Study metric, spin structure, Self-dual metric, 53C27, 53C28, [MATH.MATH-CV] Mathematics [math]/Complex Variables [math.CV], 010307 mathematical physics, Enriques–Kodaira classification, Mathematics::Differential Geometry, Parallelisable complex surface, Espace twistoriel, Fisher information metric
Abstract

In this paper we use the twistor theory in order to build non standard complex structures (with a meaning which we define) on products of 4-manifolds with the sphere of dimension two. To that end, we enumerate the set of complex surfaces whose twistor space is topologically trivial. Among these surfaces, we determine those which admit a spin structure or an anti-selfdual riemannian metric.

Published
2006

8. On the geometry of connections with totally skew-symmetric torsion on manifolds with additional tensor structures and indefinite metrics

Author

Manev, Mancho, Mekerov, Dimitar, and Gribachev, Kostadin

Subjects
*GEOMETRIC connections, *ALMOST complex manifolds, *ALMOST contact manifolds, *TORSION theory (Algebra), *MATHEMATICAL symmetry, *GEOMETRIC analysis
Abstract

Abstract: This paper is a survey of results obtained by the authors on the geometry of connections with totally skew-symmetric torsion on the following manifolds: almost complex manifolds with Norden metric, almost contact manifolds with B-metric and almost hypercomplex manifolds with Hermitian and anti-Hermitian metric. [Copyright &y& Elsevier]

Published
2011
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