Maps of manifolds with indefinite metrics preserving certain geometrical entities

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.

Keywords

• Riemannian and pseudo-Riemannian manifolds
• diffeomorphism of manifolds.