Searcharxiv⌕ Search

arXiv subjects

Gauree Shanker

Publications and source records attributed to Gauree Shanker.

At least 19 recordsLinked to original sources
arXiv2026

Cosmological Reconstruction in $f(Q, T)$ Gravity: $\Lambda$CDM Background and Matter-Sector Dependence

In this work, we investigate the cosmological reconstruction of $f(Q, T)$ gravity, where $Q$ is the non-metricity scalar and $T$ is the trace of the energy-momentum tensor. We consider the functional form $f(Q,T)=f(Q)+\lambda T$ and reconstruct explicit forms of $f(Q)$ corresponding to the $\Lambda$CDM expansion history in Friedmann-Lema\^itre-Robertson-Walker (FLRW) universe. By employing the matter conservation equation and expressing the cosmological quantities in terms of $Q$, the reconstruction problem is formulated as a first-order linear differential equation for $f(Q)$. Analytical solutions for $f(Q)$ are obtained for various matter configurations, including dust-like matter, a perfect fluid with equation-of-state parameter $\omega=-1/3$, and a nonisentropic perfect fluid with a time-dependent barotropic index. Additionally, an e-folding formulation of the reconstruction is considered to examine the cosmological evolution in terms of the e-folding parameter. The resulting forms of $f(Q)$ confirm that the $\Lambda$CDM expansion history can be successfully realized within the $f(Q,T)$ framework across diverse matter sectors.

gr-qc↗
arXiv2026

Submanifolds of Bochner Holomorphic Statistical Manifolds

In this paper, we study the submanifolds of holomorphic statistical manifolds with vanishing Bochner curvature tensor (Bochner holomorphic statistical manifolds). We study the Lagrangian statistical submanifolds and discuss their conformal flatness under the assumption of vanishing Bochner curvature tensor. Next we study the holomorphic submanifolds of Bochner holomorphic statistical manifolds and prove that the doubly autoparallel holomorphic submanifold of a Bochner holomorphic statistical manifold has vanishing Bochner curvature tensor.

math.DG↗
arXiv2025

Cosmological Dynamics of Accelerating Model in $f(T)$ Gravity with Special Forms of Deceleration Parameter

In this paper, the dynamical behavior of the accelerated expansion of the universe is discussed within the framework of $f(T)$ gravity, considering power law functional form of $ f(T)=\alpha (-T)^{n}$. Two distinct redshift-dependent parameterization of the deceleration parameter such as $q(z)=q_{0}+ q_{1}\left(\frac{ \ln(N+z)}{z+1}-\ln N \right)$ and $ q(z)=\frac{1}{2}+ \frac{q_{1}z+ q_{2}}{(1+z)^2} $ are considered. We have derived the Hubble parameter in terms of redshift and discussed its effect on other cosmological parameters. Using Bayesian statistical analysis and $\chi^2$-minimization, the median values of the model parameters for both the cosmic chronometer(CC) and the joint(CC + Pantheon) dataset have been determined. Further, energy density, pressure, the equation of state for Dark Energy, Energy condition and statefinder diagnostics are analyzed. The current age of the universe is also computed for these models.

gr-qc↗
arXiv2025

On the geometry of Riemannian warped product maps

In this paper, we begin by introducing Clairaut Riemannian warped product maps and establish the condition under which a regular curve becomes a geodesic. We obtain the conditions for a Riemannian warped product map to be Clairaut Riemannian warped product map followed by Ricci curvature. Further, we study the Ricci soliton structure on a Riemannian warped product manifold using curvature tensor. We examine the Bochner type formulae for Clairaut Riemannian warped product map and construct a supporting example. Furthermore, we extend the study to introduce and examine some geometric aspects of conformal Riemannian warped product maps. We derive the integral formula for scalar curvature of conformal Riemannian warped product map. Finally, we construct an example for conformal Riemannian warped product map.

math.DG↗
arXiv2025

On some optimal inequalities for bi-slant submanifolds in metallic Riemannian space forms

In this paper, we derive some important optimal relationships for bi-slant submanifolds in metallic Riemannian product space forms enriching the understanding of their geometric properties and deepening the connection between intrinsic and extrinsic curvature invariants. We establish generalized Wintgen inequality for bi-slant submanifolds in metallic Riemannian product space forms and discussed the equality case. Next we derive optimal inequalities involving $\delta$-invariants, also known as Chen-invariants and discuss the conditions for Chen ideal submanifolds. Further, we derive optimal relationships involving Ricci curvature and shape operator invariants along with the discussion about the equality cases. In the last section, we establish optimal inequalities involving generalized normalized $\delta$-Casorati curvatures for bi-slant submanifolds of metallic Riemannian product space form and discuss the conditions under which the equality holds. Furthermore, we examine how the main findings specialize to slant, semi-slant, hemi-slant, and semi-invariant submanifolds in metallic Riemannian product space forms, offering a better understanding of their geometric characteristics.

math.DG↗
arXiv2024

Bi-slant Riemannian maps to Kenmotsu manifolds and some optimal inequalities

In this paper, we introduce bi-slant Riemannian maps from Riemannian manifolds to Kenmotsu manifolds, which are the natural generalizations of invariant, anti-invariant, semi-invariant, slant, semi-slant and hemi-slant Riemannian maps, with nontrivial examples. We study these maps and give some curvature relations for $(rangeF_*)^\perp$. We construct Chen-Ricci inequalities, DDVV inequalities, and further some optimal inequalities involving Casorati curvatures from bi-slant Riemannian manifolds to Kenmotsu space forms.

math.DG↗
arXiv2024

Clairaut anti-invariant Riemannian maps to Sasakian manifolds

In this paper, we investigate the geometry of Clairaut anti-invariant Riemannnian maps whose base space are Sasakian manifolds. We obtain the necessary and sufficient conditions for a curve on a base manifold to be geodesic. We obtain conditions for an anti-invariant Riemannian map to be Clairaut. Further, we discuss the biharmonicity of such maps and construct some illustrative examples.

math.DG↗
arXiv2024

Clairaut anti-invariant Riemannian maps with K\"ahler and Ricci soliton structures

The aim of this article is to explore the Clairaut anti-invariant Riemannian maps from/to K\"ahler manifolds admitting Ricci solitons. We find the curvature relations and calculate the Ricci tensor under different conditions. We discuss the condition under which range space becomes $\alpha$-Ricci soliton. We obtain conditions for the range and kernel spaces of these maps to be Einstein. Next, we find the scalar curvature for range space. Further, we give the relation between Ricci curvature and Lie derivative under these maps. Moreover, we find the condition for a vertical potential vector field on target manifold to be conformal vector field on range space of these maps. Finally, we give non-trivial examples of such maps.

math.DG↗
arXiv2023

Conformal Warped Product Submersion

In this paper, the concept of Riemannian warped product submersion is generalized to the conformal case. We introduce the notion of conformal warped product submersion. It is a submersion between warped product manifolds that preserves angles between the horizontal vectors. The fundamental tensors of submersion are derived for conformal warped product submersion.

math.DG↗
arXiv2023

Clairaut slant Riemannian maps to K\"ahler manifolds

The aim of this article is to describe the idea of Clairaut slant Riemannian maps from Riemannian manifolds to K\"ahler manifolds. First, for the slant Riemannian map, we obtain the necessary and sufficient conditions for a curve to be a geodesic on the base manifold. Further, we find the necessary and sufficient conditions for the slant Riemannian map to be a Clairaut slant Riemannian map; for Clairaut slant Riemannian map to be totally geodesic; for the base manifold to be a locally product manifold. Further, we obtain the necessary and sufficient condition for the integrability of range of derivative map. Also, we investigate the harmonicity of Clairaut slant Riemannian map. Finally, we get two inequalities in terms of second fundamental form of a Clairaut slant Riemannian map and check the equality case.

math.DG↗
arXiv2023

Clairaut anti-invariant Riemannian maps to trans-Sasakian manifolds

In this article, we introduce Clairaut anti-invariant Riemannian maps from Riemannian manifolds to trans-Sasakian manifolds. We derive necessary and sufficient condition for an anti-invariant map to be Clairaut when base manifold is trans-Sasakian manifold. We discuss the integrability of range\pi_* and (range\pi_*)^\perp. Further, we establish harmonicity of these maps. Finally, we construct nontrivial examples of such maps for justification.

math.DG↗
arXiv2022

First Chen Inequality for General Warped Product Submanifolds of a Riemannian Space Form and Applications

In this paper, the first Chen inequality is proved for general warped product submanifolds in Riemannian space forms, this inequality involves intrinsic invariants ($δ$-invariant and sectional curvature) controlled by an extrinsic one (the mean curvature vector), which provides an answer for Problem 1. As a geometric application, this inequality is applied to derive a necessary condition for the immersed submanifold to be minimal in Riemannian space forms, which presents a partial answer for the well-known problem proposed by S.S. Chern, Problem 2. For further research directions, we address a couple of open problems; namely Problem 3 and Problem 4.

math.DG↗
arXiv2022

Curvatures on homogeneous Finsler spaces

The main aim of this article is to calculate explicit formula for S-curvature in homogeneous generalized m-Kropina metric. Further, we also deduce mean Berwald curvature for homogeneous generalized m-Kropina metric from S-curvature.

math.DG↗
arXiv2021

On the flag curvature of a homogeneous Finsler sapce with generalized $m$-Kropina metric

In this paper, first, we give an explicit formula for the flag curvature of a homogeneous Finsler space with generalized $m$-Kropina metric. Then, we show that, under a mild condition, the two definitions of naturally reductive homogeneous Finsler space are equivalent for afore said metric. Finally, we study the flag curvature of naturally reductive homogeneous Finsler spaces with generalized $m$-Kropina metric.

math.DG↗
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↗