A connection with parallel torsion on almost hypercomplex manifolds with Hermitian and anti-Hermitian metrics

Details A connection with parallel torsion on almost hypercomplex manifolds with Hermitian and anti-Hermitian metrics A connection with parallel torsion on almost hypercomplex manifolds with Hermitian and anti-Hermitian metrics

2008-06-24

arxiv.org/abs/0806.3831v5

Journal of Geometry and Physics 61 (2011) 248-259

Mathematics

Differential Geometry

20 pages, This paper is dedicated to Professor Kostadin Gribachev, the author's teacher in the theory of manifolds, on the occ

Scientific paper

10.1016/j.geomphys.2010.09.018

Almost hypercomplex manifolds with Hermitian and anti-Hermitian metrics are considered. A linear connection $D$ is introduced such that the structure of these manifolds is parallel with respect to D. 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 D is D-parallel. Curvature properties of these manifolds are studied. An example of 4-dimensional manifolds in the considered basic class is constructed and characterized.

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