scholarly journals Three dimensional contact metric manifolds with Cotton solitons

2021 ◽  
Vol 51 (3) ◽  
Author(s):  
Xiaomin Chen
Keyword(s):  
Three Dimensional ◽  
Contact Metric Manifolds

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 Certain results on N(k)-contact metric manifolds

2018 ◽  
Vol 49 (3) ◽  
pp. 205-220
Author(s):  
Uday Chand De
Keyword(s):  
Vector Field ◽  
Three Dimensional ◽  
Characteristic Vector ◽  
Ricci Solitons ◽  
Gradient Ricci Solitons ◽  
Contact Metric Manifolds ◽  
Nullity Distribution ◽  
Characteristic Vector Field

In the present paper we study contact metric manifolds whose characteristic vector field $\xi$ belonging to the $k$-nullity distribution. First we consider concircularly pseudosymmetric $N(k)$-contact metric manifolds of dimension $(2n+1)$. Beside these, we consider Ricci solitons and gradient Ricci solitons on three dimensional $N(k)$-contact metric manifolds. As a consequence we obtain several results. Finally, an example is given.

scholarly journals HOMOGENEOUS RIEMANNIAN STRUCTURES ON BERGER 3-SPHERES

2005 ◽  
Vol 48 (2) ◽  
pp. 375-387 ◽  
Author(s):  
P. M. Gadea ◽  
J. A. Oubiña
Keyword(s):  
Three Dimensional ◽  
Berger Spheres ◽  
Contact Metric Manifolds ◽  
Almost Contact Metric ◽  
Homogeneous Riemannian Structures ◽  
Groups Of Isometries ◽  
Almost Contact Metric Manifolds

AbstractThe homogeneous Riemannian structures on the three-dimensional Berger spheres, their corresponding reductive decompositions and the associated groups of isometries are obtained. The Berger 3-spheres are also considered as homogeneous almost contact metric manifolds.

Homogeneity on three-dimensional contact metric manifolds

1999 ◽  
Vol 114 (1) ◽  
pp. 301-321 ◽  
Author(s):  
G. Calvaruso ◽  
D. Perrone ◽  
L. Vanhecke
Keyword(s):  
Three Dimensional ◽  
Contact Metric Manifolds

CONTACT METRIC THREE-MANIFOLDS WITH CONSTANT SCALAR TORSION

2018 ◽  
Vol 107 (02) ◽  
pp. 234-255
Author(s):  
T. KOUFOGIORGOS ◽  
C. TSICHLIAS
Keyword(s):  
Three Dimensional ◽  
Local Description ◽  
Contact Metric Manifolds

In this paper we study three-dimensional contact metric manifolds satisfying $\Vert \unicode[STIX]{x1D70F}\Vert =\text{constant}$ . The local description, as well as several global results and new examples of such manifolds are given.

A classification of three dimensional $N(k)$ contact metric manifolds

2014 ◽  
Vol 39 ◽  
pp. 179-193
Author(s):  
Uday Chand De ◽  
◽  
Sujit Ghosh ◽  
Keyword(s):  
Three Dimensional ◽  
Contact Metric Manifolds

scholarly journals On three-dimensional (m,ρ)-quasi-Einstein N(k)-contact metric manifold

Filomat ◽  
2021 ◽  
Vol 35 (8) ◽  
pp. 2801-2809
Author(s):  
Avijit Sarkar ◽  
Uday De ◽  
Gour Biswas
Keyword(s):  
Sectional Curvature ◽  
Einstein Manifold ◽  
Three Dimensional ◽  
Constant Sectional Curvature ◽  
Contact Metric Manifold ◽  
Contact Metric Manifolds

(m,?)-quasi-Einstein N(k)-contact metric manifolds have been studied and it is established that if such a manifold is a (m,?)-quasi-Einstein manifold, then the manifold is a manifold of constant sectional curvature k. Further analysis has been done for gradient Einstein soliton, in particular. Obtained results are supported by an illustrative example.

The orbit of Pluto over a long interval of time

1966 ◽  
Vol 25 ◽  
pp. 227-229 ◽  
Author(s):  
D. Brouwer
Keyword(s):  
Periodic Orbit ◽  
Numerical Integration ◽  
Restricted Problem ◽  
Three Dimensional ◽  
The Third ◽  
Circular Restricted Problem ◽  
Resonance Relation

The paper presents a summary of the results obtained by C. J. Cohen and E. C. Hubbard, who established by numerical integration that a resonance relation exists between the orbits of Neptune and Pluto. The problem may be explored further by approximating the motion of Pluto by that of a particle with negligible mass in the three-dimensional (circular) restricted problem. The mass of Pluto and the eccentricity of Neptune's orbit are ignored in this approximation. Significant features of the problem appear to be the presence of two critical arguments and the possibility that the orbit may be related to a periodic orbit of the third kind.

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