A geometry with parallel skew-symmetric torsion is a Riemannian manifold carrying metric connection torsion. Besides the trivial case of Levi-Civita connection, geometries non-vanishing arise naturally in several geometric contexts, e.g. on reductive homogeneous spaces, nearly Kähler or G2-manifolds, Sasakian and 3-Sasakian manifolds, twistor spaces over quaternion-Kähler manifolds positive sca...

In this paper, we characterize N(k)-contact metric manifolds with generalized Tanaka-Webster connection. We obtain some curvature properties. It is proven that if an manifold connection K-contact then it example of Sasakian space form. Also, examine flatness and symmetric conditions concircular tensor on

In this paper, we initiate the study of conformal $\eta$-Ricci soliton and almost within framework para-Sasakian manifold. We prove that if metric admits soliton, then manifold is $\eta$-Einstein either vector field $V$ Killing or it leaves $\phi$ invariant. Here, have shown characteristics scalar curvature when admitting pointwise collinear with characteristic $\xi$. Next, show a endowed an in...