On the equivalence problem for manifolds of indefinite metrics

TL;DR

This paper investigates conditions under which indefinite Riemannian and Kaehlerian manifolds are equivalent, focusing on Ricci tensor and curvature tensor properties related to Kulkarni's problem.

Contribution

It provides new theorems characterizing manifold equivalence based on Ricci and curvature tensor values on specific vectors and planes.

Findings

Theorems for Ricci tensor values on isotropic vectors

Results for curvature tensor on degenerate holomorphic 2-planes

Conditions linking manifold equivalence to tensor properties

Abstract

Conditions, related to Kulkarni's equivalence problem are considered for indefinite Riemannian and Kaehlerian manifolds. Corresponding theorems are obtained for the values of the Ricci tensor on isotropic vectors as well as for the values of the curvature tensor on degenerate holomorphic 2-planes.