相关论文: $\eta-$Ricci solitons on contact pseudo-metric man…

A weak metric $f$-structure $(f,Q,\xi_i,\eta^i,g)\ (i=1,\ldots,s)$, generalizes the metric $f$-structure on a smooth manifold, i.e., the complex structure on the contact distribution is replaced with a nonsingular skew-symmetric tensor. We…

We extend a result of Patodi for closed Riemannian manifolds to the context of closed contact manifolds by showing the condition that a manifold is an $\eta$-Einstein Sasakian manifold is spectrally determined. We also prove that the…

Recent interest among geometers in $f$-structures of K. Yano is due to the study of topology and dynamics of contact foliations and generalized A. Weinstein conjectures. Weak metric $f$-structures, introduced by the author and R. Wolak as a…

It is well known that a unit sphere admits Sasakian 3-structure. Also, Sasakian manifolds are locally isometric to a unit sphere under several curvature and critical conditions. So, a natural question is: Does there exist any curvature or…

Almost contact complex Riemannian manifolds, also known as almost contact B-metric manifolds, are equipped with a pair of pseudo-Riemannian metrics that are mutually associated with each other using the tensor structure. Here we consider a…

Object of study are para-Ricci-like solitons on para-Sasaki-like almost paracontact almost paracomplex Riemannian manifolds, briefly, Riemannian $\Pi$-manifolds. Different cases when the potential of the soliton is the Reeb vector field or…

We study the properties of LP-Sasakian manifolds endowed with generalized $% \eta -$Ricci solitons associated to the general connection. Finally, the existence of such solitons on a 4-dimensional LP-Sasakian manifold is proved by…

Para-Ricci-like solitons with arbitrary potential on para-Sasaki-like Riemannian $\Pi$-manifolds are introduced and studied. For the studied soliton, it is proved that its Ricci tensor is a constant multiple of the vertical component of…

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 completely describe paracontact metric three-manifolds whose Reeb vector field satisfies the Ricci soliton equation. While contact Riemannian (or Lorentz\-ian) Ricci solitons are necessarily trivial, that is, $K$-contact and Einstein,…

The goal of the present paper is to deliberate certain types of metric such as $*$-$\eta$-Ricci-Yamabe soliton on $\alpha$-Cosymplectic manifolds with respect to quarter-symmetric metric connection. Further, we have proved some curvature…

We consider almost $\eta$-Ricci solitons in $(LCS)_n$-manifolds satisfying certain curvature conditions. We provide a lower and an upper bound for the norm of the Ricci curvature in the gradient case, derive a Bochner-type formula for an…

The object of the present paper is to study some properties of Kenmotsu manifold whose metric is conformal $\eta$-Einstein soliton. We have studied some certain properties of Kenmotsu manifold admitting conformal $\eta$-Einstein soliton. We…

In this paper we introduce the concept of $(\varepsilon)$-almost paracontact manifolds, and in particular, of $(\varepsilon)$-para Sasakian manifolds. Several examples are presented. Some typical identities for curvature tensor and Ricci…

We show that a Sasakian metric which also satisfies the gradient Ricci soliton equation is necessarily Einstein.

We provide properties of almost $\eta$-Ricci and almost $\eta$-Yamabe solitons on submanifolds isometrically immersed into a Riemannian manifold $\left(\widetilde{M},\widetilde{g} \right)$ whose potential vector field is the tangential…

A contact 3-manifold $M$ admitting a transversal Ricci soliton $(g,v,\lambda)$ is either Sasakian or locally isometric to one of the Lie groups SU(2), $SL(2,R)$, E(2), E(1,1) with a left invariant metric.

Considering pseudo-Riemannian $g$-natural metrics on tangent bundles, we prove that the condition of being Ricci soliton is hereditary in the sense that a Ricci soliton structure on the tangent bundle gives rise to a Ricci soliton structure…

Gradient almost para-Ricci-like solitons on para-Sasaki-like Riemannian $\Pi$-manifolds are studied. It is proved that these objects have constant soliton coefficients. For the soliton under study is shown that the corresponding scalar…

In this research, we study the nature of $\eta$-Einstein and gradient $\eta$-Einstein soliton in the framework of almost coK\"{a}hler manifolds and $(\kappa, \mu)$-almost coK\"{a}hler manifolds. We find some expressions for scalar curvature…