On the projective curvature tensor of generalized Sasakian-space-forms. (English) Zbl 1274.53067

De, Uday Chand; Sarkar, Avijit

Quaest. Math. 33, No. 2, 245-252 (2010).

Summary: The object of the present paper is to study the nature of generalized Sasakian-space-forms under some conditions regarding projective curvature tensor. All the results obtained in this paper are in the form of necessary and sufficient conditions.

MSC:

53C25	Special Riemannian manifolds (Einstein, Sasakian, etc.)
53D15	Almost contact and almost symplectic manifolds

Keywords:

Einstein manifold; generalized Sasakian-space-forms; projectively flat; projectively recurrent; projectively symmetric; projectively-semisymmetric; scalar curvature