Maps of manifolds with indefinite metrics preserving certain geometrical entities - R. S. Kulkarni (International Journal of Mathematics and Mathematical Sciences, 1978)
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.