On Conformal Kropina Transformation of m-TH Root Metrics

2021 ◽  
Vol 88 (1-2) ◽  
pp. 97
Author(s):  
Manoj Kumar ◽  
C. K. Mishra
Keyword(s):  
Projectively Flat ◽  
Metric Tensors

In this paper, we consider conformal Kropina transformation of <em>m</em>-th root metric and for this find Fundamental metric tensors and Spray coefficients. Moreover, condition for locally projectively flat on conformal Kropina transformation of <em>m</em>-th root metric has been found.

ON A PERFECT FLUID K¨ AHLER SPACETIME

2016 ◽  
Vol 12 (3) ◽  
pp. 4350-4355
Author(s):  
VIBHA SRIVASTAVA ◽  
P. N. PANDEY
Keyword(s):  
Field Equation ◽  
Perfect Fluid ◽  
Sectional Curvature ◽  
Einstein Field Equation ◽  
Cosmological Term ◽  
Conformal Killing ◽  
Killing Vectors ◽  
Projectively Flat ◽  
Conformal Killing Vectors

The object of the present paper is to study a perfect fluid K¨ahlerspacetime. A perfect fluid K¨ahler spacetime satisfying the Einstein field equation with a cosmological term has been studied and the existence of killingand conformal killing vectors have been discussed. Certain results related to sectional curvature for pseudo projectively flat perfect fluid K¨ahler spacetime have been obtained. Dust model for perfect fluid K¨ahler spacetime has also been studied.

PROJECTIVELY FLAT FINSLER METRICS WITH ALMOST ISOTROPIC S-CURVATURE

2006 ◽  
Vol 26 (2) ◽  
pp. 307-313 ◽  
Author(s):  
Xinyue Cheng ◽  
Zhongmin Shen
Keyword(s):  
Finsler Metrics ◽  
Projectively Flat

Two families of affine projectively flat surfaces

1997 ◽  
Vol 58 (1-2) ◽  
pp. 117-122 ◽  
Author(s):  
Wlodzimierz Jelonek
Keyword(s):  
Flat Surfaces ◽  
Projectively Flat

A Note on Randers Metrics of Scalar Flag Curvature

2012 ◽  
Vol 55 (3) ◽  
pp. 474-486 ◽  
Author(s):  
Bin Chen ◽  
Lili Zhao
Keyword(s):  
Scalar Curvature ◽  
Three Dimensional ◽  
Constant Scalar Curvature ◽  
Flag Curvature ◽  
Projectively Flat ◽  
Randers Metrics

AbstractSome families of Randers metrics of scalar flag curvature are studied in this paper. Explicit examples that are neither locally projectively flat nor of isotropic S-curvature are given. Certain Randers metrics with Einstein α are considered and proved to be complex. Three dimensional Randers manifolds, with α having constant scalar curvature, are studied.

scholarly journals How a projectively flat geometry regulates F(R)-gravity theory?

2021 ◽  
Author(s):  
Tee-How Loo ◽  
Avik De ◽  
Sanjay Mandal ◽  
P. K. Sahoo
Keyword(s):  
Matter Field ◽  
Gravity Theory ◽  
Gravity Models ◽  
Spacetime Geometry ◽  
Projectively Flat ◽  
Expansion Scalar ◽  
Isotropic Pressure ◽  
Constant Energy Density ◽  
Projective Flatness

Abstract In the present paper we examine a projectively flat spacetime solution of F(R)-gravity theory. It is seen that once we deploy projective flatness in the geometry of the spacetime, the matter field has constant energy density and isotropic pressure. We then make the condition weaker and discuss the effects of projectively harmonic spacetime geometry in F(R)-gravity theory and show that the spacetime in this case reduces to a generalised Robertson-Walker spacetime with a shear, vorticity, acceleration free perfect fluid with a specific form of expansion scalar presented in terms of the scale factor. Role of conharmonic curvature tensor in the spacetime geometry is also briefly discussed. Some analysis of the obtained results are conducted in terms of couple of F(R)-gravity models.

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