Curvature properties and isotropic planes of Riemannian and almost Hermitian manifolds of indefinite metrics

Details Curvature properties and isotropic planes of Riemannian and almost Hermitian manifolds of indefinite metrics Curvature properties and isotropic planes of Riemannian and almost Hermitian manifolds of indefinite metrics

2010-08-11

arxiv.org/abs/1008.1925v1

Ann. Univ. Sofia, Fac. Math. Mec. 78, 1984, 121-131

Mathematics

Differential Geometry

11 pages

Scientific paper

We study two types of isotropic planes: weakly isotropic and strongly isotropic planes. We prove that a Riemannian manifold of indefinite metric is conformally flat if and only if its curvature tensor vanishes on all the strongly isotropic planes. We specialize the plane axiom for Riemannian manifolds of indefinite metrics. We show that manifolds satisfying plane axiom of weakly (strongly) isotropic planes are of constant sectional curvature (conformaly flat). Further we study analogous problems on almost Hermitian manifolds of indefinite metrics.

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