Diffeomorphisms of pseudo-Riemannian manifolds and the values of the curvature tensor on degenerate planes

Details Diffeomorphisms of pseudo-Riemannian manifolds and the values of the curvature tensor on degenerate planes Diffeomorphisms of pseudo-Riemannian manifolds and the values of the curvature tensor on degenerate planes

2010-08-30

arxiv.org/abs/1008.5076v1

SERDICA Bulgaricae mathematicae publicationes. Vol. 15, 1989, p. 78-86

Mathematics

Differential Geometry

9 pages

Scientific paper

A diffeomorphism of pseudo-Riemannian manifolds is called sectional curvature preserving if it preserves the sectional curvature of all the nondegenerate 2-planes. We consider a similar condition for degenerate 2-planes and we prove that the diffeomorphism is conformal (when the condition is fulfilled for weakly degenerate planes) or an isometry (when the condition is fulfilled for strongly degenerate 2-planes).

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