On generalized almost para-Hermitian spaces

Abstract

Recently, a generalized almost Hermitian metric on an almost complex manifold (M, J) is determined as a generalized Riemannian metric (i.e. an arbitrary bilinear form) G which satisfies G(JX, JY) = G(X,Y), where X and Y are arbitrary vector fields on M. In the same manner we can study a generalized almost para-Hermitian metric and determine almost para-Hermitian spaces. Some properties of these spaces and special generalized almost para-Hermitian spaces including generalized para-Hermitian spaces as well as generalized nearly para-K?hler spaces are determined. Finally, a non-trivial example of generalized almost para-Hermitian space is constructed.