Certain results on invariant submanifolds of an almost Kenmotsu $$(\kappa ,\mu ,\nu )$$-space

In the present paper, we study invariant submanifolds of almost Kenmotsu structures whose Riemannian curvature tensor has $$(\kappa ,\mu ,\nu )$$ ( κ , μ , ν ) -nullity distribution. Since the geometry of an invariant submanifold inherits almost all properties of the ambient manifold, we research how the functions $$\kappa ,\mu $$ κ , μ and $$\nu $$ ν behave on the submanifold. In this connection, necessary and sufficient conditions are investigated for an invariant submanifold of an almost Kenmotsu $$(\kappa ,\mu ,\nu )$$ ( κ , μ , ν ) -space to be totally geodesic under some conditions.

Nearly cosymplectic manifolds with nullity conditions

We investigate nearly cosymplectic manifolds with [Formula: see text]-nullity distribution. Also, we consider pseudo-projectively flat [Formula: see text]-nearly cosymplectic manifold and study [Formula: see text] condition.

Certain results on N(k)-contact metric manifolds

In the present paper we study contact metric manifolds whose characteristic vector field $\xi$ belonging to the $k$-nullity distribution. First we consider concircularly pseudosymmetric $N(k)$-contact metric manifolds of dimension $(2n+1)$. Beside these, we consider Ricci solitons and gradient Ricci solitons on three dimensional $N(k)$-contact metric manifolds. As a consequence we obtain several results. Finally, an example is given.

On the quasi-conformal curvature tensor of an almost Kenmotsu manifold with nullity distributions

The object of the present paper is to characterize quasi-conformally flat and $\xi$-quasi-conformally flat almost Kenmotsu manifolds with $(k,\mu)$-nullity and $(k,\mu)'$-nullity distributions respectively. Also we characterize almost Kenmotsu manifolds with vanishing extended quasi-conformal curvature tensor and extended $\xi$-quasi-conformally flat almost Kenmotsu manifolds such that the characteristic vector field $\xi$ belongs to the $(k,\mu)$-nullity distribution.

Ricci semisymmetric almost Kenmotsu manifolds with nullity distributions

The object of the present paper is to characterize Ricci semisymmetric almost Kenmotsu manifolds with its characteristic vector field ? belonging to the (k,?)'-nullity distribution and (k,?)-nullity distribution respectively. Finally, an illustrative example is given.

A new class of f -structures satisfying f3-f=0

In this study, we introduce a new class of pseudo f -structure, called hyperbolic f -structure. We give some classifications of this new structure. Further, we extend the notion of (k,?,v)-nullity distribution to hyperbolic almost Kenmotsu f-manifolds. Finally, we construct some non-trivial examples of such manifolds.

On almost Kenmotsu manifolds with nullity distributions

The object of this paper is to characterize the curvature conditions $R\cdot P=0$ and $P\cdot S=0$ with its characteristic vector field $\xi$ belonging to the $(k,\mu)'$-nullity distribution and $(k,\mu)$-nullity distribution respectively, where $P$ is the Weyl projective curvature tensor. As a consequence of the main results we obtain several corollaries.

Second order parallel tensors on almost Kenmotsu manifolds satisfying the nullity distributions

In this paper, we prove that if there exists a second order symmetric parallel tensor on an almost Kenmotsu manifold (M2n+1, ?, ?, ?, g) whose characteristic vector field ? belongs to the (k,?)'-nullity distribution, then either M2n+1 is locally isometric to the Riemannian product of an (n+1)-dimensional manifold of constant sectional curvature -4 and a flat n-dimensional manifold, or the second order parallel tensor is a constant multiple of the associated metric tensor of M2n+1. Furthermore, some properties of an almost Kenmotsu manifold admitting a second order parallel tensor with ? belonging to the (k,?)-nullity distribution are also obtained.