Connection with parallel totally skew-symmetric torsion on almost complex manifolds with Norden metric

Details Connection with parallel totally skew-symmetric torsion on almost complex manifolds with Norden metric Connection with parallel totally skew-symmetric torsion on almost complex manifolds with Norden metric

2009-07-09

arxiv.org/abs/0907.1507v1

C. R. Acad. Bulgare Sci., 2009, 62, p.1501-1508

Mathematics

Differential Geometry

8 pages

Scientific paper

In the present work we consider an almost complex manifold with Norden metric (i.e. a metric with respect to which the almost complex structure is an antiisometry). On such a manifold we study a linear connection preserving the almost complex structure and the metric and having a totally skew-symmetric torsion tensor. We consider the case when the manifold admits a connection with parallel totally skew-symmetric torsion and the case when such connection has a Kaehler curvature tensor. We get necessary and sufficient conditions for an isotropic Kaehler manifold with Norden metric.

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