arXiv subjects

Sarita Rani

Publications and source records attributed to Sarita Rani.

7 recordsLinked to original sources

arXiv2021

On the Ricci curvature of homogeneous Finsler spaces with $(α,β)$-metrics

The study of curvature properties of homogeneous Finsler spaces with $(α, β)$-metrics is one of the central problems in Riemann-Finsler geometry. In this paper, we consider homogeneous Finsler spaces with square metric and Randers change of square metric. First, we derive the explicit formulae for Ricci curvature of homogeneous Finsler spaces with these metrics. Next, we find a necessary and sufficient condition under which a homogeneous Finsler space with either of these metrics is of vanishing $S$-curvature. The formulae for Ricci curvature of homogeneous Finsler spaces with square metric and Randers change of square metric having vanishing $S$-curvature are established. Finally, we prove that the aforesaid spaces having vanishing $S$-curvature and negative Ricci curvature must be Riemannian.

math.DG↗

arXiv2019

On $S$-Curvature of Homogeneous Finsler spaces with $(α, β)$-metrics

The study of curvature properties of homogeneous Finsler spaces with $(α, β)$-metrics is one of the central problems in Riemann-Finsler geometry. In the present paper, the existence of invariant vector fields on homogeneous Finsler spaces with square $(α, β)$-metric and Randers changed square $(α, β)$-metric is proved. Further, an explicit formula for $S$-curvature of these $(α, β)$-metrics is established. Finally, using the formula of $S$-curvature, the mean Berwald curvature of afore said $(α, β)$-metrics is calculated.

math.DG↗

arXiv2018

On the Rigidity of Spherically Symmetric Finsler Metrics with Isotropic $E$-Curvature

In the current paper, first we give the correct version of the formula for mean Berwald curvature of a spherically symmetric Finsler metric given in paper \cite{YCheWSon2015}. Further, we establish differential equations characterizing projectively as well as dually flat spherically symmetric Finsler metrics. Finally, we obtain a rigidity result on spherically symmetric Finsler metrics with isotropic $E$-Curvature.

math.DG↗

arXiv2018

Weighted quasi-metrics associated with Finsler metrics

The current paper deals with some new classes of Finsler metrics with reversible geodesics. We construct weighted quasi-metrics associated with these metrics. Further, we investigate some important geometric properties of weighted quasi-metric space. Finally, we discuss the embedding of quasi-metric spaces with generalized weight.

math.DG↗

arXiv2017

Some classes of projectively and dually flat Finsler spaces with Randers change

In this paper, we consider Randers change of some special $ (α, β)- $ metrics. First we find the fundamental metric tensor and Cartan tensor of these Randers changed $ (α, β)- $metrics. Next, we establish a general formula for inverse of fundamental metric tensors of these metrics. Finally, we find the necessary and sufficient conditions under which the Randers change of these $ (α, β)- $ metrics are projectively and locally dually flat.

math.DG↗

arXiv2016

The Bianchi type-V Dark Energy Cosmology in Self Interacting Brans Dicke Theory of Gravity

This paper deals with a spatially homogeneous and totally anisotropic Bianchi type-V cosmological model within the framework of self interacting Brans Dicke theory of gravity in the background of anisotropic dark energy (DE) with variable equation of state (EoS) parameter and constant deceleration parameter. Constant deceleration parameter leads to two models of universe, i.e. power law model and exponential model. EoS parameter ω and its existing range for the models is in good agreement with the most recent observational data. We notice that ω given by (37) i.e ω(t) = log(k1t) is more suitable in explaining the evolution of the universe. The physical behaviors of the solutions have also been discussed using some physical quantities. Finally, we observe that despite having several prominent features, both of the DE models discussed fail in details.

gr-qc↗

arXiv2015

Constraints on cosmological parameters in power-law cosmology

In this paper, we examine observational constraints on the power law cosmology; essentially dependent on two parameters $H_0$ (Hubble constant) and $q$ (deceleration parameter). We investigate the constraints on these parameters using the latest 28 points of H(z) data and 580 points of Union2.1 compilation data and, compare the results with the results of $Λ$CDM. We also forecast constraints using a simulated data set for the future JDEM, supernovae survey. Our studies give better insight into power law cosmology than the earlier done analysis by Kumar [arXiv:1109.6924] indicating it tuning well with Union2.1 compilation data but not with H(z) data. However, the constraints obtained on $ $ and $ $ i.e. $H_0$ average and $q$ average using the simulated data set for the future JDEM, supernovae survey are found to be inconsistent with the values obtained from the H(z) and Union2.1 compilation data. We also perform the statefinder analysis and find that the power-law cosmological models approach the standard $Λ$CDM model as $q\rightarrow -1$. Finally, we observe that although the power law cosmology explains several prominent features of evolution of the Universe, it fails in details.

gr-qc↗