Journal ArticleDOI
Certain types of metrics on almost coKähler manifolds
TLDR
In this article, it was shown that Bach flat almost coKahler manifold admits Ricci solitons, satisfying the critical point equation (CPE) or Bach flat.Abstract:
In this paper, we study an almost coKahler manifold admitting certain metrics such as $$*$$
-Ricci solitons, satisfying the critical point equation (CPE) or Bach flat. First, we consider a coKahler 3-manifold (M, g) admitting a $$*$$
-Ricci soliton (g, X) and we show in this case that either M is locally flat or X is an infinitesimal contact transformation. Next, we study non-coKahler $$(\kappa ,\mu )$$
-almost coKahler metrics as CPE metrics and prove that such a g cannot be a solution of CPE with non-trivial function f. Finally, we prove that a $$(\kappa , \mu )$$
-almost coKahler manifold (M, g) is coKahler if either M admits a divergence free Cotton tensor or the metric g is Bach flat. In contrast to this, we show by a suitable example that there are Bach flat almost coKahler manifolds which are non-coKahler.read more
Citations
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Journal ArticleDOI
Riemann solitons on almost co-Kähler manifolds
TL;DR: In this article , it was shown that if the metric of an almost co-K?hler manifold is a Riemann soliton with the soliton vector field, then the manifold is flat.
Journal ArticleDOI
Generalized Ricci soliton and paracontact geometry
TL;DR: In this article, the authors studied generalized Ricci soliton in the framework of paracontact metric manifolds and proved that the scalar curvature r is constant and the squared norm of Ricci operator is constant.
Journal ArticleDOI
Critical point equation on almost f-cosymplectic manifolds
TL;DR: In this article, the authors considered CPE on almost f-cosymplectic manifolds and proved that the CPE conjecture is true for almost f cosymetric manifolds.
Journal ArticleDOI
Almost *-η-Ricci solitons on Kenmotsu pseudo-Riemannian manifolds
Singh Rashmi,V. Venkatesha +1 more
TL;DR: In this paper , a special class of contact pseudo-Riemannian manifold, called almost * {*} -η-Ricci solitons, is studied and shown to be an Einstein manifold if the potential vector field V is an infinitesimal contact transformation.
References
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Journal ArticleDOI
The Critical Point Equation And Contact Geometry
TL;DR: In this paper, the authors considered the CPE conjecture in the frame-work of contact manifold and contact metric and proved that a complete contact metric satisfying the conjecture is Einstein and is isometric to a unit sphere.
Journal ArticleDOI
Sasakian manifolds with purely transversal Bach tensor
Amalendu Ghosh,Ramesh Sharma +1 more
TL;DR: In this article, it was shown that a (2n + 1)-dimensional Sasakian manifold with a purely transversal Bach tensor has constant scalar curvature ≥ 2n(2n+1), equality holding if and only if (M, g) is Einstein.
Journal ArticleDOI
$*$-Ricci solitons and gradient almost $*$-Ricci solitons on Kenmotsu manifolds
TL;DR: In this paper, the authors consider the case where the potential vector field is collinear with the characteristic vector field on an open set of manifolds and show that the potential field is equal to the soliton vector field.
Posted Content
Para-Sasakian manifolds and *-Ricci solitons
TL;DR: In this paper, a special type of metric called *-Ricci soliton on a para-Sasakian manifold was studied, and it was shown that if the *-Sakian metric is a Ricci tensor on a manifold M, then M is either D-homothetic to an Einstein manifold, or the Ricci metric vanishes.
Journal ArticleDOI
Non-existence of $$*$$ ∗ -Ricci solitons on $$(\kappa ,\mu )$$ ( κ , μ ) -almost cosymplectic manifolds
TL;DR: In this paper, the authors prove a non-existence result for Ricci solitons on non-cosymplectic manifolds, and prove the same result for almost cosympelous manifolds.