Generalized Sasakian-space-forms with projective curvature tensor

The object of the present paper is to study φ-projectively flat generalized Sasakian-space-forms, projectively locally symmetric generalized Sasakian-space-forms and projectively locally φ-symmetric generalized Sasakian-space-forms. All the obtained results are in the form of necessary and sufficient conditions. Interesting relations between projective curvature tensor and conformal curvature tensor of a generalized Sasakian-spaceform of dimension greater than three have been established. Some of these properties are also analyzed in the light of quarter-symmetric metric connection, in addition with the Levi-Civita connection. Obtained results are supported by illustrative examples.