Generalized Lorentzian Sasakian-Space-Forms with <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="bold-script">M</mi></mrow></semantics></math></inline-formula>-Projective Curvature Tensor

Abstract

In this note, the generalized Lorentzian Sasakian-space-form M12n+1(f1,f2,f3) satisfying certain constraints on the M-projective curvature tensor W* is considered. Here, we characterize the structure M12n+1(f1,f2,f3) when it is, respectively, M-projectively flat, M-projectively semisymmetric, M-projectively pseudosymmetric, and φ−M-projectively semisymmetric. Moreover, M12n+1(f1,f2,f3) satisfies the conditions W*(ζ,V1)·S=0, W*(ζ,V1)·R=0 and W*(ζ,V1)·W*=0 are also examined. Finally, illustrative examples are given for obtained results.

Keywords

• contact Lorentzian manifold
• generalized Lorentzian Sasakian-space-form
• ℳ-projective curvature tensor