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International Journal of Mathematics and Mathematical Sciences
Volume 1, Issue 1, Pages 137-140
http://dx.doi.org/10.1155/S0161171278000174

Maps of manifolds with indefinite metrics preserving certain geometrical entities

Department of Mathematics, Indiana University, Bloomington, Indiana 47401, USA

Received 1 June 1977

Copyright © 1978 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

It is shown that (i) a diffeomorphism of manifolds with indefinite metrics preserving degenerate r-plane sections is conformal, (ii) a sectional curvature-preservlng diffeomorphism of manifolds with indefinite metrics of dimension 4 is generically an isometry.