scholarly journals Certain Class of Almost α -Cosymplectic Manifolds

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Sermin Öztürk ◽  
Hakan Öztürk
Keyword(s):  
Conformally Flat ◽  
Cosymplectic Manifolds ◽  
Flat Condition

This paper concerned with almost α -cosymplectic manifolds satisfying conformally flat condition. Firstly, we investigate Kaehler integral submanifolds of almost α -cosymplectic manifolds. Next, we study conformally flat almost α -cosymplectic manifolds of dim ≥ 5 whose integral submanifolds are Kaehler. Finally, an illustrative example is constructed to verify our result.

Study of conformally flat polytropes with tilted congruence

2018 ◽  
Vol 27 (07) ◽  
pp. 1850063 ◽  
Author(s):  
M. Sharif ◽  
Sobia Sadiq
Keyword(s):  
Equation Of State ◽  
Matter Content ◽  
Energy Conditions ◽  
Spherically Symmetric ◽  
Conformally Flat ◽  
Flat Condition ◽  
Polytropic Equation ◽  
Dissipative Fluid ◽  
Symmetric Spacetime ◽  
Fluid Configuration

This paper is aimed to study the modeling of spherically symmetric spacetime in the presence of anisotropic dissipative fluid configuration. This is accomplished for an observer moving relative to matter content using two cases of polytropic equation-of-state under conformally flat condition. We formulate the corresponding generalized Tolman–Oppenheimer–Volkoff equation, mass equation, as well as energy conditions for both cases. The conformally flat condition is imposed to find an expression for anisotropy which helps to study spherically symmetric polytropes. Finally, Tolman mass is used to analyze stability of the resulting models.

scholarly journals Para-CR structures on almost paracontact metric manifolds

2014 ◽  
Vol 20 (2) ◽  
Author(s):  
Joanna Wełyczko
Keyword(s):  
Sectional Curvature ◽  
Sufficient Conditions ◽  
Sasakian Manifold ◽  
Necessary And Sufficient Conditions ◽  
Constant Sectional Curvature ◽  
Conformally Flat ◽  
Cr Manifolds ◽  
Cosymplectic Manifolds ◽  
Cr Structures ◽  
Necessary And Sufficient

AbstractAlmost paracontact metric manifolds are the famous examples of almost para-CR manifolds. We find necessary and sufficient conditions for such manifolds to be para-CR. Next we examine these conditions in certain subclasses of almost paracontact metric manifolds. Especially, it is shown that normal almost paracontact metric manifolds are para-CR. We establish necessary and sufficient conditions for paracontact metric manifolds as well as for almost para-cosymplectic manifolds to be para-CR. We find also basic curvature identities for para-CR paracontact metric manifolds and study their consequences. Among others, we prove that any para-CR paracontact metric manifold of constant sectional curvature and of dimension greater than 3 must be para-Sasakian and its curvature equal to -1. The last assertion does not hold in dimension 3. We show that a conformally flat para-Sasakian manifold is of constant sectional curvature equal to -1. New classes of examples of para-CR manifolds are established.

Effects of charge on anisotropic conformally flat polytropes

2015 ◽  
Vol 93 (11) ◽  
pp. 1420-1426 ◽  
Author(s):  
M. Sharif ◽  
Sobia Sadiq
Keyword(s):  
Electromagnetic Field ◽  
Equations Of State ◽  
Compact Object ◽  
Spherically Symmetric ◽  
Conformally Flat ◽  
Matter Distribution ◽  
Anisotropic Matter ◽  
Flat Condition

In this paper, we study the effects of electromagnetic field on conformally flat spherically symmetric anisotropic matter distribution satisfying two polytropic equations of state. We consider conformally flat condition and evaluate corresponding anisotropy, which is used to study polytropes for the charged compact object. Finally, we study stability of the resulting models using the Tolman mass. It is concluded that only one of the resulting models is physically viable.

Conformally flat polytropes for anisotropic cylindrical geometry

2015 ◽  
Vol 93 (12) ◽  
pp. 1583-1587 ◽  
Author(s):  
M. Sharif ◽  
Sobia Sadiq
Keyword(s):  
Gravitational Potential ◽  
Equations Of State ◽  
Graphical Analysis ◽  
Cylindrical Geometry ◽  
Energy Conditions ◽  
Conformally Flat ◽  
Matter Distribution ◽  
Anisotropic Matter ◽  
Cylindrically Symmetric ◽  
Flat Condition

In this paper, we study cylindrically symmetric anisotropic matter distribution satisfying two polytropic equations of state. The corresponding Lane–Emden equations are constructed and the energy conditions are checked. We evaluate a particular expression for anisotropy by using the conformally flat condition, which helps in the study of polytropic models. The graphical analysis of surface gravitational potential indicates the increasing behavior of model compactness. Finally, we conclude that one of the obtained models is physically viable.

Study of stellar structures in f(ℛ,𝒯μν𝒯μν) theory

2021 ◽  
Author(s):  
M. Sharif ◽  
M. Zeeshan Gul
Keyword(s):  
Specific Model ◽  
Fluid Distribution ◽  
Anisotropic Fluid ◽  
Anisotropic Pressure ◽  
Conformally Flat ◽  
Flat Condition ◽  
Correction Terms ◽  
Physical Quantities ◽  
Cylindrical Collapse ◽  
Fluid Parameters

This paper deals with the dynamics of cylindrical collapse with anisotropic fluid distribution in the framework of [Formula: see text] gravity. For this purpose, we consider non-static and static cylindrical spacetimes in the inner and outer regions of a star, respectively. To match both geometries at the hypersurface, we consider the Darmois junction conditions. We use the Misner–Sharp technique to examine the impacts of correction terms and effective fluid parameters on the dynamics of a cylindrical star. A correlation between the Weyl tensor and physical quantities is also developed. The conformally flat condition is not obtained due to the influence of anisotropic pressure and higher-order nonlinear terms. Further, we assume isotropic fluid and specific model of this theory which yields the conformally flat spacetime and inhomogeneous energy density. We conclude that the collapse rate reduces as compared to general relativity due to the inclusion of effective pressure and additional terms of this theory.

scholarly journals Analysis of the Conformally Flat Approximation for Binary Neutron Star Initial Conditions

2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
In-Saeng Suh ◽  
Grant J. Mathews ◽  
J. Reese Haywood ◽  
N. Q. Lan
Keyword(s):  
Neutron Stars ◽  
Initial Conditions ◽  
State Dependence ◽  
Einstein Equations ◽  
Conformally Flat ◽  
Binary Neutron Star ◽  
Stable Circular Orbit ◽  
Flat Condition ◽  
Binary Neutron Stars ◽  
The Stability

The spatially conformally flat approximation (CFA) is a viable method to deduce initial conditions for the subsequent evolution of binary neutron stars employing the full Einstein equations. Here we analyze the viability of the CFA for the general relativistic hydrodynamic initial conditions of binary neutron stars. We illustrate the stability of the conformally flat condition on the hydrodynamics by numerically evolving ~100 quasicircular orbits. We illustrate the use of this approximation for orbiting neutron stars in the quasicircular orbit approximation to demonstrate the equation of state dependence of these initial conditions and how they might affect the emergent gravitational wave frequency as the stars approach the innermost stable circular orbit.

Curvature inequalities for C-totally real doubly warped products of locally conformal almost cosymplectic manifolds

Filomat ◽  
2017 ◽  
Vol 31 (20) ◽  
pp. 6449-6459 ◽  
Author(s):  
Akram Ali ◽  
Siraj Uddin ◽  
Wan Othman ◽  
Cenap Ozel
Keyword(s):  
Sectional Curvature ◽  
Mean Curvature ◽  
Warped Product ◽  
Warped Products ◽  
Equality Case ◽  
Cosymplectic Manifolds ◽  
Almost Cosymplectic Manifold ◽  
Locally Conformal ◽  
Totally Real ◽  
Optimal Inequalities

In this paper, we establish some optimal inequalities for the squared mean curvature in terms warping functions of a C-totally real doubly warped product submanifold of a locally conformal almost cosymplectic manifold with a pointwise ?-sectional curvature c. The equality case in the statement of inequalities is also considered. Moreover, some applications of obtained results are derived.

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