Related papers: On Generalized m-th Root Finsler Metrics

In this paper, we study one of the open problems in Finsler geometry which presented by Matsumoto-Shimada about the existence of P-reducible metric which is not C-reducible. For this aim, we study a class of Finsler metrics called…

We consider the projective Finsler metrizability problem: under what conditions the solutions of a given system of second-order ordinary differential equations (SODE) coincide with the geodesics of a Finsler metric, as oriented curves.…

We apply topological methods and a Lusternik-Schnirelmann-type approach to prove existence results for closed geodesics of Finsler metrics on spheres and projective spaces. The main tool in the proofs are spherical complexities, which have…

In this paper we will show that the generalized connected sum construction for constant scalar curvature metrics can be extended to the zero scalar curvature case. In particular we want to construct solutions to the Yamabe equation on the…

In this paper, we consider a special class of singular Finsler metrics: $m$-Kropina metrics which are defined by a Riemannian metric and a $1$-form. We show that an $m$-Kropina metric ($m\ne -1$) of scalar flag curvature must be locally…

We prove that the normal metric contact pairs with orthogonal characteristic foliations, which are either Bochner flat or locally conformally flat, are locally isometric to the Hopf manifolds. As a corollary we obtain the classification of…

First we present a short overview of the long history of projectively flat Finsler spaces. We give a simple and quite elementary proof of the already known condition for the projective flatness, and we give a criterion for the projective…

Generalized integral formulas involving the generalized Bessel-Maitland function are considered and it expressed in terms of generalized Wright hypergeometric functions. By assuming appropriate values of the parameters in the main results,…

Robotics research has found numerous important applications of Riemannian geometry. Despite that, the concept remain challenging to many roboticists because the background material is complex and strikingly foreign. Beyond {\em Riemannian}…

We present a uniform framework generalising and extending the classical theories of projective differential geometry, c-projective geometry, and almost quaternionic geometry. Such geometries, which we call \emph{projective parabolic…

The well-known Funk metric F(x,y) is projectively flat with constant flag curvature K=-1/4 and the Hilbert metric H(x,y):=(F(x,y)+F(x,-y))/2 is projectively flat with constant curvature K=-1. These metrics are the special solutions to…

We study (generalized) cones over metric spaces, both in Riemannian and Lorentzian signature. In particular, we establish synthetic lower Ricci curvature bounds \`a la Lott-Villani-Sturm and Ohta in the metric measure case, and \`a la…

Our results concern geometry of a manifold endowed with a pair of complementary orthogonal distributions (plane fields) and a time-dependent Riemannian metric. The work begins with formulae concerning deformations of geometric quantities as…

Let $M$ be a smooth manifold, let $TM$ be its tangent bundle and $T^{*}M$ its cotangent bundle. This paper investigates integrability conditions for generalized metrics, generalized almost para-complex structures, and generalized Hermitian…

In this paper, I will show how to use $\beta$-deformations to deal with dual flatness of $(\alpha,\beta)$-metrics. It is a natural continuation of the research on dually flat Randers metrics(see arxiv:1209.1150). $\beta$-deformations is a…

Fixed point results with respect to generalized rational contractive mappings in semi-metric spaces endowed with a directed graph are proved. Some examples are provided to illustrate the results. The obtained results extend, improve and…

The flag curvature is a natural extension of the sectional curvature in Riemannian geometry, and the S-curvature is a non-Riemannian quantity which vanishes for Riemannian metrics. There are (incomplete) non-Riemannian Finsler metrics on an…

Let $(M,g_M,\mathcal F)$ be a closed, connected Riemannian manifold with a Riemannian foliation $\mathcal F$ of nonzero constant transversal scalar curvature. When $M$ admits a transversal nonisometric conformal field, we find some…

In this paper, we introduce horizontal and vertical warped product Finsler manifold. We prove that every C-reducible or proper Berwaldian doubly warped product Finsler manifold is Riemannian. Then, we find the relation between Riemmanian…

Comparisons on $L^{n\over 2}$-norms of scalar curvatures between Riemannian metrics and standard metrics are obtained. The metrics are restricted to conformal classes or under certain curvature conditions.