We study canonical paracontact connection on a para-Sasakian manifold. We prove that a Ricci-flat para-Sasakian manifold with respect to canonical paracontact connection is an η-Einstein manifold.We also investigate some properties of curvature tensor, conformal curvature tensor,W2curvature tensor, concircular curvature tensor, projective curvature tensor, and pseudo-projective curvature tensor...

In this paper we consider pseudo projectively flat Riemannian manifold whose Ricci tensor S satisfies the condition S(X,Y ) = rT (X)T (Y ), where r is the scalar curvature, T is a non-zero 1-form defined by g(X, ξ) = T (X), ξ is a unit vector field and prove that the manifold is of pseudo quasi constant curvature, integral curves of the vector field ξ are geodesic and ξ is a proper concircular ...

In the present study, we considered 3-dimensional generalized (κ, μ)-contact metric manifolds. We proved that a 3-dimensional generalized (κ, μ)-contact metric manifold is not locally φ-symmetric in the sense of Takahashi. However such a manifold is locally φ-symmetric provided that κ and μ are constants. Also it is shown that if a 3-dimensional generalized (κ, μ) -contact metric manifold is Ri...

we study umbilic (space-like) submanifolds of pseudo-riemannian space forms, then define totally semi-umbilic space-like submanifold of pseudo euclidean space and relate this notion to umbilicity. finally we give characterization of total semi-umbilicity for space-like submanifolds contained in pseudo sphere or pseudo hyperbolic space or the light cone.a pseudo-riemannian submanifold m in (a ps...

Object of the present paper is to study pseudo Hermitian magnetic curves in (κ,µ) manifold admitting Zamkovoy connection. We give main classification theorem for pseudo-Hermitian curve. Again we find curvature and torsion a (κ,µ)-manifold

In an earlier paper we developed the classification of weakly symmetric pseudo–Riemannian manifolds $G/H$, where $G$ is a semisimple Lie group and $H$ reductive subgroup. We derived from cases compact. As consequence obtained Lorentz signature $(n-1,1)$ trans-Lorentzian $(n-2,2)$. Here work out pseudo-Riemannian nilmanifolds $G/H$ for case $G=N \rtimes H$ with compact $N$ nilpotent. It turns th...