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Ranadip Gangopadhyay

Publications and source records attributed to Ranadip Gangopadhyay.

10 recordsLinked to original sources
arXiv2026

On Locally Dually and Projectively Flat Almost Rational Finsler Metrics

In this paper, we investigate Almost Rational Finsler (AR-Finsler) metrics, a class of Finsler metrics whose fundamental tensor admits a decomposition $g_{ij}(x,y)=η(x,y)a_{ij}(x,y),$ where $η$ is a positive smooth function and $a_{ij}$ is rational in the fiber variables. We derive necessary and sufficient conditions for local dual flatness and local projective flatness of AR-Finsler metrics. Furthermore, we obtain a compatibility relation characterizing AR-Finsler metrics that are simultaneously locally dually flat and locally projectively flat. As an application, we establish a rigidity result for AR-Finsler. Motivated by these results and several known rigidity phenomena in special classes of Finsler metrics, we formulate a conjecture concerning the local Minkowskianity of AR-Finsler metrics that are both locally dually flat and locally projectively flat. Several examples are presented to illustrate the theory.

math.DG↗
arXiv2025

On the Cartan torsion of Minkowskian product of Finsler manifolds

In this paper, we investigate the Cartan torsion and mean Cartan torsion of the Minkowskian product of two Finsler metrics. We derive explicit formulas for both torsions and analyze their geometric behavior. In particular, we demonstrate that both the Cartan torsion and mean Cartan torsion decompose additively if and only if the Minkowskian product is Euclidean. Additionally, we provide a necessary and sufficient condition for the norm of the mean Cartan torsion to remain bounded in the Euclidean case.

math.DG↗
arXiv2024

On Minkowskian Product Einstein-Finsler spaces

In this paper we study the Minkowskian product Finsler manifolds. More precisely, we prove that if the Minkowskian product Finsler manifold is Einstein then either the product manifold is Ricci flat or both the quotient manifolds are Einstein with same scalar functions.

math.DG↗
arXiv2023

The Isoperimetric Problem in Randers Poincaré Disc

It is known that a simply connected Riemann surface satisfies the isoperimetric equality if and only if it has constant Gaussian curvature. In this article, we show that Randers Poincaré disc satisfies the isoperimetric equality with respect to different volume forms. These metrics do not necessarily have constant (negative) flag curvature. Thus we show that the Osserman's result \cite{RO} in the Riemannian case can not be extended to the corresponding Finslerian case.

math.DG↗
arXiv2022

The Isoperimetric Problem In Randers Planes

In this paper, the isoperimetric problem in Randers planes, $(\mathbb{R}^2,F=α+β)$, which are slight deformation of the Euclidean plane $(\mathbb{R}^2,α)$ by suitable one forms $β$, have been studied. We prove that the circles centred at the origin achieves the local maximum area of the isoperimetric problem with respect to well known volume forms in Finsler geometry.

math.DG↗
arXiv2022

On Minimal Surfaces of Revolutions Immersed in Deformed Hyperbolic Kropina Space

In this paper we consider three dimensional upper half space $\mathbb{H}^3 $ equipped with various Kropina metrics obtained by deformation of hyperbolic metric of $\mathbb{H}^3$ through $1$-forms and obtain a partial differential equation that characterizes minimal surfaces immersed in it. We prove that such minimal surfaces can only be obtained when the hyperbolic metric is deformed along $x^3$ direction. Then we classify such minimal surfaces and show that flag curvature of these surfaces is always non-positive. We also obtain the geodesics of this surface. In particular, it follows that such surfaces neither have forward conjugate points nor they are forward complete.

math.DG↗
arXiv2021

On C3-Like Finsler Metrics Under Ricci Flow

In this paper we have studied the class of Finsler metrics, called C3-like metrics which satisfy the un-normal and normal Ricci flow equation and proved that such metrics are Einstein.

math.DG↗
arXiv2021

On minimal surfaces immersed in three dimensional Kropina Minkowski space

In this paper we consider a three dimensional Kropina space and obtain the partial differential equation that characterizes a minimal surfaces with the induced metric. Using this characterization equation we study various immersions of minimal surfaces. In particular, we obtain the partial differential equation that characterizes the minimal translation surfaces and show that the plane is the only such surface.

math.DG↗
arXiv2020

Minimal surfaces in three-dimensional Matsumoto space

In this paper we consider the Matsumoto metric $F=\frac{α^2}{α-β}$, on the three dimensional real vector space and obtain the partial differential equations that characterize the minimal surfaces which are graphs of smooth functions and then we prove that plane is the only such surface. We also obtain the partial differential equation that characterizes the minimal translation surfaces and show that again plane is the only such surface.

math.DG↗