scholarly journals RICCI SOLITONS ON THREE-DIMENSIONAL $\eta$-EINSTEIN ALMOST KENMOTSU MANIFOLDS

2015 ◽  
Vol 19 (1) ◽  
pp. 91-100 ◽  
Author(s):  
Yaning Wang ◽  
Ximin Liu
Keyword(s):  
Three Dimensional ◽  
Ricci Solitons ◽  
Kenmotsu Manifolds ◽  
Almost Kenmotsu Manifolds

scholarly journals Almost Kenmotsu 3-h-manifolds with transversely Killing-type Ricci operators

2020 ◽  
Vol 18 (1) ◽  
pp. 1056-1063
Author(s):  
Quanxiang Pan ◽  
Hui Wu ◽  
Yajie Wang
Keyword(s):  
Lie Group ◽  
Ricci Tensor ◽  
Three Dimensional ◽  
Local Symmetry ◽  
Ricci Operator ◽  
Kenmotsu Manifolds ◽  
Almost Kenmotsu Manifolds ◽  
Parallel Ricci Tensor

Abstract In this paper, it is proved that the Ricci operator of an almost Kenmotsu 3-h-manifold M is of transversely Killing-type if and only if M is locally isometric to the hyperbolic 3-space {{\mathbb{H}}}^{3}(-1) or a non-unimodular Lie group endowed with a left invariant non-Kenmotsu almost Kenmotsu structure. This result extends those results obtained by Cho [Local symmetry on almost Kenmotsu three-manifolds, Hokkaido Math. J. 45 (2016), no. 3, 435–442] and Wang [Three-dimensional locally symmetric almost Kenmotsu manifolds, Ann. Polon. Math. 116 (2016), no. 1, 79–86; Three-dimensional almost Kenmotsu manifolds with \eta -parallel Ricci tensor, J. Korean Math. Soc. 54 (2017), no. 3, 793–805].

scholarly journals A class of 3-dimensional almost Kenmotsu manifolds with harmonic curvature tensors

2016 ◽  
Vol 14 (1) ◽  
pp. 977-985 ◽  
Author(s):  
Yaning Wang
Keyword(s):  
Recent Result ◽  
Three Dimensional ◽  
Local Symmetry ◽  
Kenmotsu Manifold ◽  
Harmonic Curvature ◽  
Riemannian Product ◽  
3 Dimensional ◽  
Kenmotsu Manifolds ◽  
Almost Kenmotsu Manifolds ◽  
Curvature Tensors

AbstractLet M3 be a three-dimensional almost Kenmotsu manifold satisfying ▽ξh = 0. In this paper, we prove that the curvature tensor of M3 is harmonic if and only if M3 is locally isometric to either the hyperbolic space ℍ3(-1) or the Riemannian product ℍ2(−4) × ℝ. This generalizes a recent result obtained by [Wang Y., Three-dimensional locally symmetric almost Kenmotsu manifolds, Ann. Polon. Math., 2016, 116, 79-86] and [Cho J.T., Local symmetry on almost Kenmotsu three-manifolds, Hokkaido Math. J., 2016, 45, 435-442].

A note on invariant submanifolds of CR-integrable almost Kenmotsu manifolds

Filomat ◽  
2017 ◽  
Vol 31 (19) ◽  
pp. 6211-6218 ◽  
Author(s):  
Young Suh ◽  
Krishanu Mandal ◽  
Uday De
Keyword(s):  
Invariant Submanifold ◽  
Kenmotsu Manifold ◽  
Totally Geodesic ◽  
Almost Kenmotsu Manifold ◽  
Kenmotsu Manifolds ◽  
Almost Kenmotsu Manifolds ◽  
Invariant Submanifolds

The present paper deals with invariant submanifolds of CR-integrable almost Kenmotsu manifolds. Among others it is proved that every invariant submanifold of a CR-integrable (k,?)'-almost Kenmotsu manifold with k < -1 is totally geodesic. Finally, we construct an example of an invariant submanifold of a CR-integrable (k,?)'-almost Kenmotsu manifold which is totally geodesic.

scholarly journals Three-dimensional Lorentzian homogeneous Ricci solitons

2011 ◽  
Vol 188 (1) ◽  
pp. 385-403 ◽  
Author(s):  
M. Brozos-Vázquez ◽  
G. Calvaruso ◽  
E. García-Río ◽  
S. Gavino-Fernández
Keyword(s):  
Three Dimensional ◽  
Ricci Solitons
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