scholarly journals Conformal flatness of circle bundle metric

1998 ◽  
Vol 22 (2) ◽  
pp. 349-355
Author(s):  
Takafumi Satou
Keyword(s):  
Circle Bundle ◽  
Conformal Flatness

scholarly journals Bochner and conformal flatness of normal metric contact pairs

2015 ◽  
Vol 48 (1) ◽  
pp. 47-56 ◽  
Author(s):  
Gianluca Bande ◽  
David E. Blair ◽  
Amine Hadjar
Keyword(s):  
Conformal Flatness

Study of tilted anisotropic polytropes

2019 ◽  
Vol 28 (03) ◽  
pp. 1950051
Author(s):  
M. Sharif ◽  
Sobia Sadiq
Keyword(s):  
Equations Of State ◽  
Conservation Equation ◽  
Specific Form ◽  
Energy Conditions ◽  
Spherically Symmetric ◽  
Conformally Flat ◽  
Anisotropic Matter ◽  
Conformal Flatness ◽  
Energy Bound ◽  
Aids Study

The purpose of this paper is to construct spherically symmetric models for anisotropic matter configurations by imposing conformally flat conditions. This work is done for a relatively moving observer with matter using two types of polytropic equations of state. We evaluate the corresponding conservation equation, mass equation as well as energy constraints for both choices of equations of state. The conformal flatness is employed to find a specific form of anisotropy which aids study to spherical polytropic configurations. It is found that the first model satisfies all the energy conditions while the second model does not meet the dominant energy bound. It is also found that both models remain stable throughout the evolution.

scholarly journals Invariants of Legendrian Knots in Circle Bundles

2003 ◽  
Vol 05 (04) ◽  
pp. 569-627 ◽  
Author(s):  
Joshua M. Sabloff
Keyword(s):  
Contact Structure ◽  
Homology Class ◽  
Graded Algebra ◽  
Legendrian Knots ◽  
Contact Homology ◽  
Circle Bundle ◽  
Differential Graded Algebra ◽  
Circle Bundles ◽  
Standard Contact ◽  
Definition Of

Let M be a circle bundle over a Riemann surface that supports a contact structure transverse to the fibers. This paper presents a combinatorial definition of a differential graded algebra (DGA) that is an invariant of Legendrian knots in M. The invariant generalizes Chekanov's combinatorial DGA invariant of Legendrian knots in the standard contact 3-space using ideas from Eliashberg, Givental, and Hofer's contact homology. The main difficulty lies in dealing with what are ostensibly 1-parameter families of generators for the DGA; these are solved using "Morse–Bott" techniques. As an application, the invariant is used to distinguish two Legendrian knots that are smoothly isotopic, realize a nontrivial homology class, but are not Legendrian isotopic.

scholarly journals Binary Neutron Stars: Equilibrium Models beyond Spatial Conformal Flatness

2006 ◽  
Vol 97 (17) ◽  
Author(s):  
Kōji Uryū ◽  
François Limousin ◽  
John L. Friedman ◽  
Eric Gourgoulhon ◽  
Masaru Shibata
Keyword(s):  
Neutron Stars ◽  
Equilibrium Models ◽  
Conformal Flatness ◽  
Binary Neutron Stars
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