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

Ognian Kassabov

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arXiv · 1008.5076

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

Ognian Kassabov

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Abstract

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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BibTeX RIS

Ognian Kassabov. 2010-08-30. Diffeomorphisms of pseudo-Riemannian manifolds and the values of the curvature tensor on degenerate planes. https://arxiv.org/abs/1008.5076

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