A connection with parallel totally skew-symmetric torsion on a class of almost hypercomplex manifolds with hermitian and anti-hermitian metrics
Mancho Manev,Kostadin Gribachev +1 more
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In this article, 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.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 Kahler 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.read more
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Natural connection with totally skew-symmetric torsion on almost contact manifolds with b-metric
TL;DR: In this paper, a natural connection with totally skew-symmetric torsion on almost contact manifolds with B-metric was constructed, and the class of these manifolds where the considered connection exists was determined.
Journal ArticleDOI
Natural connection with totally skew-symmetric torsion on almost contact manifolds with B-metric
TL;DR: In this paper, a natural connection with totally skew-symmetric torsion on almost contact manifolds with B-metric was constructed, and the class of these manifolds where the considered connection exists was determined.
Posted ContentDOI
On Geometry of Manifolds with Some Tensor Structures and Metrics of Norden Type
TL;DR: In this article, the authors studied the tensor structures of smooth Riemannian manifolds with almost contact 3-structures and Hermitian-Norden type and their relationship with natural connections having totally skew-symmetric torsion.
Journal ArticleDOI
Associated Nijenhuis Tensors on Manifolds with Almost Hypercomplex Structures and Metrics of Hermitian–Norden Type
Mancho Manev,Mancho Manev +1 more
TL;DR: In this article, an associated Nijenhuis tensor of endomorphisms in the tangent bundle is introduced and a geometric interpretation of the vanishing of these tensors is given as a necessary and sufficient condition for the existence of a unique linear connection with totally skew-symmetric torsion tensor preserving the structure.
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Manifolds with almost contact 3-structure and metrics of Hermitian-Norden type
Mancho Manev,Mancho Manev +1 more
TL;DR: In this article, the authors introduced a differentiable manifold with almost contact 3-structure, which consists of an almost contact metric structure and two almost contact B-metric structures.
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Thomas Friedrich,Stefan Ivanov +1 more
TL;DR: In this article, all almost contact metric, almost hermitian and G2-structures admit a connection with totally skew-symmetric torsion tensor, and prove that there exists at most one such connection.
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