Some Curvature Properties of Generalized Complex Space Forms

Abstract

The object of the present paper is to study generalized complex space forms satisfying curvature identities named Walker type identities. Also It is proved that the difference tensor R. ̃ – ̃.R and the Tachibana tensor Q(S, ̃) of any generalized complex space form M(f1, f2) of dimensional m ≥ 4 are linearly dependent at every point of M(f1, f2). Finally generalized complex space forms are studied under the condition R.R – Q(S,R) = L Q(g , ̃).