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

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

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

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

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.

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.

scholarly journals Fretting Wear Behavior of Three Kinds of Rubbers under Sphere-On-Flat Contact

Materials ◽  
2021 ◽  
Vol 14 (9) ◽  
pp. 2153
Author(s):  
Tengfei Zhang ◽  
Jie Su ◽  
Yuanjie Shu ◽  
Fei Shen ◽  
Liaoliang Ke
Keyword(s):  
Normal Force ◽  
Wear Behavior ◽  
Displacement Amplitude ◽  
Fretting Wear ◽  
Butadiene Rubber ◽  
Force Frequency ◽  
Sealing Performance ◽  
Rubber Surface ◽  
Sealing Materials ◽  
Flat Contact

Rubbers are widely used in various fields as the important sealing materials, such as window seal, door seal, valve, pump seal, etc. The fretting wear behavior of rubbers has an important effect on their sealing performance. This paper presents an experimental study on the fretting wear behavior of rubbers against the steel ball under air conditions (room temperature at 20 ± 2 °C and humidity at 40%). Three kinds of rubbers, including EPDM (ethylene propylene diene monomer), FPM (fluororubber), and NBR (nitrile–butadiene rubber), are considered in experiments. The sphere-on-flat contact pattern is used as the contact model. The influences of the displacement amplitude, normal force, frequency, and rubber hardness on the fretting wear behavior are discussed in detail. White light profiler and scanning electron microscope (SEM) are used to analyze the wear mechanism of the rubber surface. The fretting wear performances of three rubbers are compared by considering the effect of the displacement amplitude, normal force, frequency, and rubber hardness. The results show that NBR has the most stable friction coefficient and the best wear resistance among the three rubbers.

scholarly journals $L^{p}$ harmonic 1-forms on conformally flat Riemannian manifolds

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Jing Li ◽  
Shuxiang Feng ◽  
Peibiao Zhao
Keyword(s):  
Riemannian Manifold ◽  
Riemannian Manifolds ◽  
Schrödinger Operators ◽  
Schrodinger Operators ◽  
Finiteness Theorem ◽  
Conformally Flat ◽  
Locally Conformally Flat ◽  
Flat Riemannian Manifold ◽  
Ricci Form

AbstractIn this paper, we establish a finiteness theorem for $L^{p}$ L p harmonic 1-forms on a locally conformally flat Riemannian manifold under the assumptions on the Schrödinger operators involving the squared norm of the traceless Ricci form. This result can be regarded as a generalization of Han’s result on $L^{2}$ L 2 harmonic 1-forms.

scholarly journals New conformally flat initial data for spinning black holes

2002 ◽  
Vol 65 (10) ◽  
Author(s):  
Sergio Dain ◽  
Carlos O. Lousto ◽  
Ryoji Takahashi
Keyword(s):  
Black Holes ◽  
Initial Data ◽  
Conformally Flat
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