Journal ArticleDOI
Certain types of metrics on almost coKähler manifolds
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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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TL;DR: In this paper, the authors studied the structure of almost cosymplectic manifolds and proved that such manifolds do not exist in dimensions greater than three and gave necessary and sufficient conditions for an almost contact metncstructure to be cosymetric.
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TL;DR: An up-to-date overview of geometric and topological properties of cosymplectic and coKaehler manifolds is given in this paper, where the authors also mention some of their applications to time-dependent mechanics.
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TL;DR: An up-to-date overview of geometric and topological properties of cosymplectic and coKahler manifolds is given in this article, where the authors also mention some of their applications to time-dependent mechanics.
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Topology of Co-symplectic/Co-Kähler Manifolds
TL;DR: In this paper, the authors reveal the topology of co-symplectic/co-Kahler manifolds via symplectic/kahler mapping tori and prove the theorem of Theorem 1.