Certain results on Kenmotsu pseudo-metric manifolds
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In this article, a systematic study of Kenmotsu pseudo-metric manifolds is presented, and the Ricci solitons on these manifolds are considered, and necessary and sufficient conditions for them to have constant curvatures are provided.Abstract:
In this paper, a systematic study of Kenmotsu pseudo-metric manifolds are introduced. After studying the properties of this manifolds, we provide necessary and sufficient condition for Kenmotsu pseudo-metric manifold to have constant $\varphi$-sectional curvature, and prove the structure theorem for $\xi$-conformally flat and $\varphi$-conformally flat Kenmotsu pseudo-metric manifolds. Next, we consider Ricci solitons on this manifolds. In particular, we prove that an $\eta$-Einstein Kenmotsu pseudo-metric manifold of dimension higher than 3 admitting a Ricci soliton is Einstein, and a Kenmotsu pseudo-metric 3-manifold admitting a Ricci soliton is of constant curvature $-\varepsilon$.read more
Citations
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Riemann solitons and almost Riemann solitons on almost Kenmotsu manifolds
TL;DR: In this paper, the authors studied the Riemann soliton and gradient almost-Riemann-soliton on a certain class of almost Kenmotsu manifolds.
Journal ArticleDOI
Ricci solitons on Riemannian manifolds admitting certain vector field
TL;DR: In this article, it was shown that a Riemannian manifold equipped with a concurrent-recurrent vector field is of constant negative curvature when its metric is a Ricci soliton.
Journal ArticleDOI
Almost α -Cosymplectic Pseudo Metric Manifolds
Sermin Öztürk,Hakan Öztürk +1 more
TL;DR: The main purpose of as mentioned in this paper is to study almost cosymplectic pseudo-metric manifold satisfying certain - parallel tensor fields and obtain some results related to the - parallelity of,, and.
References
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Almost contact structures and curvature tensors
Dirk Janssens,Lieven Vanhecke +1 more
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Sasakian manifold with pseudo-Riemannian metric
TL;DR: In this article, the authors define a Sasakian manifold with pseudo-Riemannian metric, and discuss the classification of the manifold with constant φ-sectional curvatures, and prove that such a manifold is of constant curvature.
Journal ArticleDOI
Almost Kenmotsu manifolds and local symmetry
Giulia Dileo,Anna Maria Pastore +1 more
TL;DR: In this paper, the authors consider locally symmetric almost Kenmotsu manifold and show that the manifold is locally isometric to the Riemannian product of an n+1-dimensional manifold of constant curvature.