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.

H-curvature tensors on IK-normal complex contact metric manifolds

2018 ◽  
Vol 15 (12) ◽  
pp. 1850205 ◽  
Author(s):  
Aysel Turgut Vanli ◽  
Inan Unal
Keyword(s):  
Sectional Curvature ◽  
Constant Sectional Curvature ◽  
Theoretical Physics ◽  
Contact Metric Manifold ◽  
Contact Manifolds ◽  
Normal Complex ◽  
Contact Metric Manifolds ◽  
Curvature Tensors

IK-normal complex contact metric manifolds have some important properties. There are several applications of this kind of contact manifolds in theoretical physics. In this paper, we studied on [Formula: see text]-curvature tensors for IK-normal complex contact metric manifolds. We have shown that there is no IK-normal complex contact metric manifold with constant sectional curvature and an IK-normal complex contact metric manifold is not Ricci semi-symmetric.

scholarly journals Trans-Sasakian 3-Manifolds with Reeb Flow Invariant Ricci Operator

Mathematics ◽  
2018 ◽  
Vol 6 (11) ◽  
pp. 246
Author(s):  
Yan Zhao ◽  
Wenjie Wang ◽  
Ximin Liu
Keyword(s):  
Sectional Curvature ◽  
Three Dimensional ◽  
Sasakian Manifold ◽  
Constant Sectional Curvature ◽  
Ricci Operator ◽  
Cosymplectic Manifold

Let M be a three-dimensional trans-Sasakian manifold of type ( α , β ) . In this paper, we obtain that the Ricci operator of M is invariant along Reeb flow if and only if M is an α -Sasakian manifold, cosymplectic manifold or a space of constant sectional curvature. Applying this, we give a new characterization of proper trans-Sasakian 3-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 Some curvature tensors in N(k)-contact metric manifold

BIBECHANA ◽  
2018 ◽  
Vol 16 ◽  
pp. 55-63
Author(s):  
Riddhi Jung Shah
Keyword(s):  
Ricci Tensor ◽  
Einstein Manifold ◽  
Contact Metric Manifold ◽  
3 Dimensional ◽  
Contact Metric Manifolds ◽  
Curvature Tensors

The purpose of this paper is to study W7and W9-curvature tensors on N(k)-contact metric manifolds. We prove that a N(k)-contact metric manifold satisfying the condition W7( xi,X).W9=0 is eta-Einstein manifold. We also obtain the Ricci tensor S of type (0, 2) for phi-W9flat and divW9=0 conditions on N(k)-contact metric manifolds. Finally, we give an example of 3-dimensional N(k)-contact metric manifold.BIBECHANA 16 (2019) 55-63

scholarly journals Stability of contact metric manifolds and unit vector fields of minimum energy

2007 ◽  
Vol 76 (2) ◽  
pp. 269-283 ◽  
Author(s):  
D. Perrone ◽  
L. Vergori
Keyword(s):  
Vector Field ◽  
Sectional Curvature ◽  
Minimum Energy ◽  
Energy Functional ◽  
Holomorphic Sectional Curvature ◽  
Sasakian Manifolds ◽  
Contact Metric Manifold ◽  
Reeb Vector ◽  
Reeb Vector Field ◽  
Contact Metric Manifolds

In this paper we obtain criteria of stability for ηEinstein k-contact manifolds, for Sasakian manifolds of constant ϕ-sectional curvature and for 3-dimensional Sasakian manifolds. Moreover, we show that a stable compact Einstein contact metric manifold M is Sasakian if and only if the Reeb vector field ξ minimises the energy functional. In particular, the Reeb vector field of a Sasakian manifold M of constant ϕ-holomorphic sectional curvature +1 minimises the energy functional if and only if M is not simply connected.

scholarly journals RICCI SOLITONS AND CONTACT METRIC MANIFOLDS

2012 ◽  
Vol 55 (1) ◽  
pp. 123-130 ◽  
Author(s):  
AMALENDU GHOSH
Keyword(s):  
Vector Field ◽  
Sectional Curvature ◽  
Ricci Soliton ◽  
Ricci Solitons ◽  
Conformally Flat ◽  
Contact Metric Manifold ◽  
Potential Vector ◽  
Contact Metric Manifolds ◽  
Potential Vector Field

AbstractWe study on a contact metric manifold M2n+1(ϕ, ξ, η, g) such that g is a Ricci soliton with potential vector field V collinear with ξ at each point under different curvature conditions: (i) M is of pointwise constant ξ-sectional curvature, (ii) M is conformally flat.

scholarly journals Totally umbilical hypersurfaces of Spinc manifolds carrying special spinor fields

2020 ◽  
Vol 31 (12) ◽  
pp. 2050100
Author(s):  
Nadine Große ◽  
Roger Nakad
Keyword(s):  
Sectional Curvature ◽  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Einstein Manifold ◽  
Constant Sectional Curvature ◽  
Killing Spinor ◽  
Totally Umbilical ◽  
Totally Umbilical Hypersurfaces ◽  
Spinor Fields

Under some dimension restrictions, we prove that totally umbilical hypersurfaces of Spin[Formula: see text] manifolds carrying a parallel, real or imaginary Killing spinor are of constant mean curvature. This extends to the Spin[Formula: see text] case the result of Kowalski stating that, every totally umbilical hypersurface of an Einstein manifold of dimension greater or equal to [Formula: see text] is of constant mean curvature. As an application, we prove that there are no extrinsic hypersheres in complete Riemannian [Formula: see text] manifolds of non-constant sectional curvature carrying a parallel, Killing or imaginary Killing spinor.

Yamabe solitons on 3-dimensional contact metric manifolds with Qφ = φQ

2019 ◽  
Vol 16 (03) ◽  
pp. 1950039 ◽  
Author(s):  
V. Venkatesha ◽  
Devaraja Mallesha Naik
Keyword(s):  
Vector Field ◽  
Scalar Curvature ◽  
Constant Scalar Curvature ◽  
Sasakian Manifold ◽  
Contact Metric Manifold ◽  
Reeb Vector Field ◽  
3 Dimensional ◽  
Flow Vector ◽  
Contact Metric Manifolds ◽  
Yamabe Soliton

If [Formula: see text] is a 3-dimensional contact metric manifold such that [Formula: see text] which admits a Yamabe soliton [Formula: see text] with the flow vector field [Formula: see text] pointwise collinear with the Reeb vector field [Formula: see text], then we show that the scalar curvature is constant and the manifold is Sasakian. Moreover, we prove that if [Formula: see text] is endowed with a Yamabe soliton [Formula: see text], then either [Formula: see text] is flat or it has constant scalar curvature and the flow vector field [Formula: see text] is Killing. Furthermore, we show that if [Formula: see text] is non-flat, then either [Formula: see text] is a Sasakian manifold of constant curvature [Formula: see text] or [Formula: see text] is an infinitesimal automorphism of the contact metric structure on [Formula: see text].

Sign in / Sign up

Export Citation Format

Share Document