Journal ArticleDOI
Certain types of metrics on almost coKähler manifolds
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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
∗-Ricci Soliton within the frame-work of Sasakian and (κ,μ)-contact manifold
TL;DR: In this article, it was shown that if a complete Sasakian metric is an almost gradient ∗-Ricci soliton, then it is either positive or null-Sakian.
Journal ArticleDOI
On Bach flat warped product Einstein manifolds
Qiang Chen,Chenxu He +1 more
TL;DR: In this paper, it was shown that a compact warped product with vanishing Bach tensor of dimension n = 4 is a finite quotient of a warp product with $(n-1)$-dimensional Einstein fiber.
Journal ArticleDOI
∗-Ricci solitons and gradient almost ∗-Ricci solitons on Kenmotsu manifolds
TL;DR: In this paper, the authors considered the case of *-Ricci soliton in the framework of a Kenmotsu manifold and proved that soliton constant λ is zero.
Posted Content
Total Scalar Curvature and Harmonic Curvature
TL;DR: In this article, it was shown that if the critical point metric has harmonic curvature, then it is isometric to a standard sphere, and this conjecture was proved in 1984 by Besse, but has yet to be proved.