Related papers: On contact pseudo-metric manifolds satisfying a nu…
In this paper we classify Ricci-generalized pseudosymmetric $(\kappa, \mu)$-contact metric manifolds in the sense of Deszcz .
Contact metric $(\kappa ,\mu )$-spaces are generalizations of Sasakian spaces. We introduce a weak $(\kappa ,\mu )$ condition as a generalization of the K-contact one and show that many of the known results from generalized Sasakian…
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…
In this paper, we prove that evry 3-dimensional manifold M is a ?- recurrent N(k)-contact metric manifold if and only if it is flat. Then we classify the ?-recurrent contact metric manifolds of constant curvature. This implies that there…
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…
In this article, we study and analyze the \phi-sectional curvature induced by a statistical structure on an almost contact metric manifold. We demonstrate that this sectional curvature is always non-positive. Additionally, we present…
Many authors have studied Ricci solitons and their analogs within the framework of (almost) contact geometry. In this article, we thoroughly study the $(m,\rho)$-quasi-Einstein structure on a contact metric manifold. First, we prove that if…
We construct a Wick-type deformation quantization of contact metric manifolds. The construction is fully canonical and involves no arbitrary choice. Unlike the case of symplectic or Poisson manifolds, not every classical observable on a…
Let $(\varphi_\alpha,\xi_\alpha,g)$ for $\alpha=1,2$, and $3$ be a contact metric $3$-structure on the manifold $M^{4n+3}$. We show that the $3$-contact distribution of this structure admits a HyperKahler structure whenever…
The present paper deals with the study of generalized $\phi$-recurrent generalized $(k,\mu)$-contact metric manifolds with the existence of such notion by a proper example.
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 study the foliated structure of a contact metric $(\kappa,\mu)$-space. In particular, using the theory of Legendre foliations, we give a geometric interpretation to the Boeckx's classification of contact metric…
In this study, we investigate generalized quasi-Einstein structure for normal metric contact pair manifolds. Firstly, we deal with elementary properties and examine, existence, and characterizations of generalized quasi-Einstein normal…
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 consider Riemannian $n$-manifolds $M$ with nontrivial $\kappa$-nullity "distribution" of the curvature tensor $R$, namely, the variable rank distribution of tangent subspaces to $M$ where $R$ coincides with the curvature tensor of a…
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…
We introduce and study a special class of almost contact metric manifolds, which we call anti-quasi-Sasakian (aqS). Among the class of transversely K\"ahler almost contact metric manifolds $(M,\varphi, \xi,\eta,g)$, quasi-Sasakian and…
In this paper, we derive a partial result related to a question of Yau: "Does a simply-connected complete K\"ahler manifold M with negative sectional curvature admit a bounded non-constant holomorphic function?" Main Theorem. Let $M^{2n}$…
In 1972, K. Kenmotsu studied a class of almost contact Riemannian manifolds. Later, such a manifold was called a Kenmotsu manifold. This paper, we studied Kenmotsu manifolds with $(2n+s)$-dimensional $s-$contact metric manifold and this…
We investigate 3-dimensional almost Kenmotsu manifolds satisfying special types of nullity conditions depending on two smooth functions $\kappa,\mu$. When either $\kappa<-1$ and $\mu=0$ or $h=0$, such conditions coincide with the…