Related papers: Paracontact metric manifolds without a contact met…
We study paracontact metric $(\kappa,\mu)$-spaces with $\kappa=-1$, equivalent to $h^2=0$ but not $h=0$. In particular, we will give an alternative proof of Theorem 3.2 of [11] and present examples of paracontact metric $(-1,2)$-spaces and…
We study a remarkable class of paracontact metric manifolds which have no contact metric counterpart: the paracontact metric $(-1,\widetilde\mu)$-spaces which are not paraSasakian (i.e. have $\widetilde h\neq0$). We present explicit…
We give a local classification of generalized (kappa,mu)-Paracontact Metric Manifold which satisfies the condition xi(mu)=0. An example of such manifolds is presented.
The paper is a complete study of paracontact metric manifolds for which the Reeb vector field of the underlying contact structure satisfies a nullity condition (the condition \eqref{paranullity} below, for some real numbers $% \tilde\kappa$…
This paper is a study of three-dimensional paracontact metric (\k{appa},{\mu},{\nu})-manifolds. Three dimensional paracontact metric manifolds whose Reeb vector field {\xi} is harmonic are characterized. We focus on some curvature…
In this paper, we aim to introduce and study $(\kappa, \mu)$-contact pseudo-metric manifold and prove that if the $\varphi$-sectional curvature of any point of $M$ is independent of the choice of $\varphi$-section at the point, then it is…
It is provided an overview of existed results concerning classification of contact metric, almost cosymplectic and almost Kenmotsu $(\kappa,\mu)$-manifolds. In the case of dimension three it is described in full details structure of contact…
Starting from $g$-natural pseudo-Riemannian metrics of suitable signature on the unit tangent sphere bundle $T_1 M$ of a Riemannian manifold $(M,\langle,\rangle)$, we construct a family of paracontact metric structures. We prove that this…
The author is planning if possible classify all three-dimensional $(\kappa,\mu)$-manifolds wether contact metric, almost cosymplectic, para-contact metric, almost para-cosymplectic. Of course classification in contact or almost cosymplectic…
We prove that any contact metric $(\kappa,\mu)$-space $(M,\xi,\phi,\eta,g)$ admits a canonical paracontact metric structure which is compatible with the contact form $\eta$. We study such canonical paracontact structure, proving that it…
We prove that any non-Sasakian contact metric (\kappa,\mu)-space admits a canonical \eta-Einstein Sasakian or \eta-Einstein paraSasakian metric. An explicit expression for the curvature tensor fields of those metrics is given and we find…
We show that a $3-$dimensional paracontact manifold on which $Q\varphi =\varphi Q$ is either a manifold with $trh^2=0$, flat or of constant $\xi-$sectional curvature $k\neq-1$ and constant $\varphi$-sectional curvature $-k\neq 1$.
In this paper, we obtain Chen's inequalities for submanifolds in $(\kappa,\mu)$-contact space form with two kinds of generalized semi-symmetric non-metric connections.
We present a classification of the complete, simply connected, contact metric $(\kappa,\mu)$-spaces as homogeneous contact metric manifolds, by studying the base space of their canonical fibration. According to the value of the Boeckx…
In this paper, $N(\kappa)$-contact metric manifolds satisfying the conditions $\widetilde{C}(\xi,X)\cdot\widetilde{C}=0$, $\widetilde{C}(\xi,X)\cdot R=0$, $\widetilde{C}(\xi,X)\cdot S=0$, $\widetilde{C}(\xi,X)\cdot C=0$, $C\cdot S=0$ and…
We regard a contact metric manifold whose Reeb vector field belongs to the $(\kappa,\mu)$-nullity distribution as a bi-Legendrian manifold and we study its canonical bi-Legendrian structure. Then we characterize contact metric…
We characterize biharmonic anti-invariant surfaces in $3$-dimensional generalized $(\kappa, \mu)$-manifolds with non-zero constant mean curvature by means of the scalar curvature of the ambient space and the mean curvature. In addition, we…
Almost paracontact metric manifolds are the famous examples of almost para-CR manifolds. We find necessary and suffcient conditions for such manifolds to be para-CR. Next we examine these conditions in certain subclasses of almost…
The object of the present study is to study 3-dimensional generalized ($\kappa ,\mu $)-contact metric manifolds with $\tilde{W}\cdot R=0$ and $\tilde{W}\cdot H=0$ to cover all the eight equivalent classes given in \cite{Shaikh2}.
In this paper, we present a classification of $ N(\kappa)$-contact metric manifolds with using some special flatness conditions on $ \mathcal{T} $-curvature tensor. We examine $\mathcal{T}$-flat, quasi-$\mathcal{T}$-flat, $…