Three-dimensional homogeneous Lorentzian metrics with prescribed Ricci tensor

2007 ◽  
Vol 48 (12) ◽  
pp. 123518 ◽  
Author(s):  
Giovanni Calvaruso
Keyword(s):  
Ricci Tensor ◽  
Three Dimensional ◽  
Lorentzian Metrics

scholarly journals On inextensible flows of tangent developable of biharmonic B-Slant helices according to Bishop frames in the special 3-dimensional Kenmotsu manifold

2011 ◽  
Vol 31 (1) ◽  
pp. 89 ◽  
Author(s):  
Vedat Asil ◽  
Talat Körpınar ◽  
Essin Turhan
Keyword(s):  
Ricci Tensor ◽  
Three Dimensional ◽  
Kenmotsu Manifold ◽  
3 Dimensional ◽  
Developable Surfaces ◽  
Tangent Developable ◽  
Inextensible Flows ◽  
Parallel Ricci Tensor

In this paper, we study inextensible flows of tangent developable surfaces of biharmonic B-slant helices in the special three-dimensional Kenmotsu manifold K with η-parallel ricci tensor. We express some interesting relations about inextensible flows of this surfaces.

CERTAIN RESULTS ON THREE-DIMENSIONAL CONTACT METRIC MANIFOLDS

2010 ◽  
Vol 03 (04) ◽  
pp. 577-591 ◽  
Author(s):  
Amalendu Ghosh
Keyword(s):  
Ricci Tensor ◽  
Three Dimensional ◽  
Tensor Fields ◽  
Contact Metric Manifold ◽  
Ricci Operator ◽  
3 Dimensional ◽  
Contact Metric Manifolds ◽  
Parallel Ricci Tensor

In this paper we study 3-dimensional contact metric manifolds satisfying certain conditions on the tensor fields *-Ricci tensorS*, h(= ½Lξφ), τ(= Lξg = 2hφ) and the Ricci operator Q. First, we prove that a 3-dimensional non-Sasakian contact metric manifold satisfies. [Formula: see text] (where ⊕X,Y,Z denotes the cyclic sum over X,Y,Z) if and only if M is a generalized (κ, μ)-space. Next, we prove that a 3-dimensional contact metric manifold with vanishing *-Ricci tensor is a generalized (κ, μ)-space. Finally, some results on 3-dimensional contact metric manifold with cyclic η-parallel h or cyclic η-parallel τ or η-parallel Ricci tensor are presented.

scholarly journals Some characterizations of three-dimensional trans-Sasakian manifolds admitting η- Ricci solitons and trans-Sasakian manifolds as Kagan subprojective space

2020 ◽  
Vol 72 (3) ◽  
pp. 427-432
Author(s):  
A. Sarkar ◽  
A. Sil ◽  
A. K. Paul
Keyword(s):  
Curvature Tensor ◽  
Ricci Tensor ◽  
Three Dimensional ◽  
Ricci Soliton ◽  
Second Order ◽  
Ricci Solitons ◽  
Riemann Curvature ◽  
Sasakian Manifolds ◽  
Riemann Curvature Tensor ◽  
Order Parallel

UDC 514.7 The object of the present paper is to study three-dimensional trans-Sasakian manifolds admitting η -Ricci soliton. Actually, we study such manifolds whose Ricci tensor satisfy some special conditions like cyclic parallelity, Ricci semisymmetry, ϕ -Ricci semisymmetry, after reviewing the properties of second order parallel tensors on such manifolds. We determine the form of Riemann curvature tensor of trans-Sasakian manifolds of dimension greater than three as Kagan subprojective spaces. We also give some classification results of trans-Sasakian manifolds of dimension greater than three as Kagan subprojective spaces.

Real Hypersurfaces in ℂP 2 and ℂH 2 with Cyclic Parallel ∗-Ricci Tensor

2021 ◽  
Vol 58 (3) ◽  
pp. 308-318
Author(s):  
Yaning Wang ◽  
Wenjie Wang
Keyword(s):  
Ricci Tensor ◽  
Hyperbolic Plane ◽  
Real Hypersurface ◽  
Three Dimensional ◽  
Real Hypersurfaces ◽  
Complex Projective Plane ◽  
Cyclic Parallel Ricci Tensor ◽  
Complex Projective ◽  
Parallel Ricci Tensor ◽  
Complex Hyperbolic Plane

In this paper, we prove that the ∗-Ricci tensor of a real hypersurface in complex projective plane ℂP 2 or complex hyperbolic plane ℂH 2 is cyclic parallel if and only if the hypersurface is of type (A). We find some three-dimensional real hypersurfaces having non-vanishing and non-parallel ∗-Ricci tensors which are cyclic parallel.

∗-Ricci tensor on almost Kenmotsu 3-manifolds

2020 ◽  
Vol 17 (13) ◽  
pp. 2050196
Author(s):  
Dibakar Dey ◽  
Pradip Majhi
Keyword(s):  
Lie Group ◽  
Ricci Tensor ◽  
Three Dimensional ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Addition Formula ◽  
Kenmotsu Manifold ◽  
Ricci Operator ◽  
Necessary And Sufficient ◽  
Parallel Ricci Tensor

In this paper, we obtain the expressions of the ∗-Ricci operator of a three-dimensional almost Kenmotsu manifold [Formula: see text] and find that the ∗-Ricci tensor is not symmetric for [Formula: see text]. We obtain a necessary and sufficient condition for the ∗-Ricci tensor to be symmetric and proved that if the ∗-Ricci tensor of a non-Kenmotsu almost Kenmotsu 3-[Formula: see text]-manifold [Formula: see text] is symmetric, then [Formula: see text] is locally isometric to a three-dimensional non-unimodular Lie group equipped with a left invariant non-Kenmotsu almost Kenmotsu structure. Further, it is shown that the ∗-Ricci tensor of a non-Kenmotsu almost Kenmotsu 3-manifold [Formula: see text] is parallel if and only if [Formula: see text] is ∗-Ricci flat. In addition, [Formula: see text] satisfying [Formula: see text] is locally isometric to [Formula: see text]. Finally, we discuss about [Formula: see text]-parallel ∗-Ricci tensor on almost Kenmotsu 3-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].

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