Invariant Submanifolds of Generalized Sasakian-Space-Forms

The object of this paper is to study the invariant submanifolds of generalized Sasakian-space-forms. Here, we obtain some equivalent conditions for an invariant submanifold of a generalized Sasakian-space-forms to be totally geodesic.Comment: 11 page

On weak symmetries of Kenmotsu Manifolds with respect to quarter-symmetric metric connection

The aim of this paper is to study weakly symmetries of Kenmotsu man- ifolds with respect to quarter-symmetric metric connection. We investigate the properties of weakly symmetric, weakly Ricci-symmetric and weakly concircular Ricci-symmetric Kenmotsu manifolds with respect to quarter symmetric metric connection and obtain interesting results

Generalized Lorentzian Sasakian-Space-Forms with M-Projective Curvature Tensor

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