Conformally flat contact metric manifolds

2001 ◽  
Vol 70 (1) ◽  
pp. 66-76 ◽  
Author(s):  
Amalendu Ghosh ◽  
Themis Koufogiorgos ◽  
Ramesh Sharma
Keyword(s):  
Conformally Flat ◽  
Contact Metric Manifolds ◽  
Flat Contact

On conformally flat contact metric manifolds

2004 ◽  
Vol 79 (1-2) ◽  
pp. 75-88 ◽  
Author(s):  
Florence Gouli-Andreou ◽  
Niki Tsolakidou
Keyword(s):  
Conformally Flat ◽  
Contact Metric Manifolds ◽  
Flat Contact

scholarly journals Conharmonic Curvature Tensor on -Contact Metric Manifolds

ISRN Geometry ◽  
2011 ◽  
Vol 2011 ◽  
pp. 1-11 ◽  
Author(s):  
Sujit Ghosh ◽  
U. C. De ◽  
A. Taleshian
Keyword(s):  
Curvature Tensor ◽  
Contact Metric Manifolds ◽  
Conharmonic Curvature Tensor ◽  
Flat Contact

The object of the present paper is to characterize -contact metric manifolds satisfying certain curvature conditions on the conharmonic curvature tensor. In this paper we study conharmonically symmetric, -conharmonically flat, and -conharmonically flat -contact metric manifolds.

Two classes of conformally flat contact metric 3-manifolds

1999 ◽  
Vol 64 (1-2) ◽  
pp. 80-88 ◽  
Author(s):  
Florence Gouli-Andreou ◽  
Philippos J. Xenos
Keyword(s):  
Conformally Flat ◽  
Flat Contact

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.

A Class of Conformally flat Contact Metric 3-Manifolds

2003 ◽  
Vol 43 (1-2) ◽  
pp. 114-120
Author(s):  
Florence Gouli-Andreou ◽  
Ramesh Sharma
Keyword(s):  
Conformally Flat ◽  
Flat Contact

CONFORMALLY FLAT CONTACT THREE-MANIFOLDS

2016 ◽  
Vol 103 (2) ◽  
pp. 177-189 ◽  
Author(s):  
JONG TAEK CHO ◽  
DONG-HEE YANG
Keyword(s):  
Constant Curvature ◽  
Smooth Function ◽  
Sasakian Manifold ◽  
Conformally Flat ◽  
Flat Manifold ◽  
Smooth Functions ◽  
Flat Contact

In this paper, we consider contact metric three-manifolds $(M;\unicode[STIX]{x1D702},g,\unicode[STIX]{x1D711},\unicode[STIX]{x1D709})$ which satisfy the condition $\unicode[STIX]{x1D6FB}_{\unicode[STIX]{x1D709}}h=\unicode[STIX]{x1D707}h\unicode[STIX]{x1D711}+\unicode[STIX]{x1D708}h$ for some smooth functions $\unicode[STIX]{x1D707}$ and $\unicode[STIX]{x1D708}$, where $2h=\unicode[STIX]{x00A3}_{\unicode[STIX]{x1D709}}\unicode[STIX]{x1D711}$. We prove that if $M$ is conformally flat and if $\unicode[STIX]{x1D707}$ is constant, then $M$ is either a flat manifold or a Sasakian manifold of constant curvature $+1$. We cannot extend this result for a smooth function $\unicode[STIX]{x1D707}$. Indeed, we give such an example of a conformally flat contact three-manifold which is not of constant curvature.

scholarly journals Remarkable Classes of Almost 3-Contact Metric Manifolds

Axioms ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 8
Author(s):  
Giulia Dileo
Keyword(s):  
Geometric Properties ◽  
New Class ◽  
Contact Metric Manifolds ◽  
Cosymplectic Manifolds ◽  
Sasaki Manifolds

We introduce a new class of almost 3-contact metric manifolds, called 3-(0,δ)-Sasaki manifolds. We show fundamental geometric properties of these manifolds, analyzing analogies and differences with the known classes of 3-(α,δ)-Sasaki (α≠0) and 3-δ-cosymplectic manifolds.

Conformally flat kähler spaces

2020 ◽  
Author(s):  
O. Lesechko ◽  
O. Latysh ◽  
T. Spychak
Keyword(s):  
Conformally Flat

On Lagrangian Catenoids

2007 ◽  
Vol 50 (3) ◽  
pp. 321-333 ◽  
Author(s):  
David E. Blair
Keyword(s):  
General Problem ◽  
Lagrangian Submanifolds ◽  
Minimal Submanifold ◽  
Conformally Flat ◽  
Totally Geodesic ◽  
Schouten Tensor ◽  
Multiplicity One

AbstractRecently I. Castro and F.Urbano introduced the Lagrangian catenoid. Topologically, it is ℝ × Sn–1 and its induced metric is conformally flat, but not cylindrical. Their result is that if a Lagrangian minimal submanifold in ℂn is foliated by round (n – 1)-spheres, it is congruent to a Lagrangian catenoid. Here we study the question of conformally flat, minimal, Lagrangian submanifolds in ℂn. The general problem is formidable, but we first show that such a submanifold resembles a Lagrangian catenoid in that its Schouten tensor has an eigenvalue of multiplicity one. Then, restricting to the case of at most two eigenvalues, we show that the submanifold is either flat and totally geodesic or is homothetic to (a piece of) the Lagrangian catenoid.

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