Related papers: On Horizontal Recurrent Finsler Connections

The aim of the present paper is to construct and investigate a Finsler structure within the framework of a Generalized Absolute Parallelism space (GAP-space). The Finsler structure is obtained from the vector fields forming the…

Let (M_1,F_1) and (M_2,F_2) be a pair of Finsler manifolds. The Minkowskian product Finsler manifold (M,F) of (M_1,F_1) and (M_2,F_2) with respect to a product function f is the product manifold M=M_1\times M_2 endowed with the Finsler…

The aim of the present paper is to provide an intrinsic investigation of two special Finsler spaces whose defining properties are related to Berwald connection, namely, Finsler space of scalar curvature and of constant curvature. Some…

In this paper, a class of holomorphic invariant metrics is introduced on the irreducible classical domains of type I-IV, which are strongly pseudoconvex complex Finsler metrics in the strict sense of M. Abate and G. Patrizio[2]. These…

A nonlinear splitting on a fibre bundle is a generalization of an Ehresmann connection. An example is given by the homogeneous nonlinear splitting of a Finsler function on the total manifold of a fibre bundle. We show how homogeneous…

A linear connection on a Lie algebroid is called a Cartan connection if it is suitably compatible with the Lie algebroid structure. Here we show that a smooth connected manifold $M$ is locally homogeneous - i.e., admits an atlas of charts…

We show that on every Spin(7) manifold there always exists a unique linear connection with totally skew-symmetric torsion preserving a nontrivial spinor and the Spin(7) structure. We express its torsion and the Riemannian scalar curvature…

We characterize the existence of horizontal path lifts for general connections on arbitrary fiber bundles with a new property that also gives fresh insight into linear and $G$-connections.

We review the language of differential forms and their applications to Riemannian Geometry with an orientation to General Relativity. Working with the principal algebraic and differential operations on forms, we obtain the structure…

We show global uniqueness in the fractional Calder\'on problem with a single measurement and with data on arbitrary, possibly disjoint subsets of the exterior. The previous work \cite{GhoshSaloUhlmann} considered the case of infinitely many…

In this paper, first we prove the existence of invariant vector field on a homogeneous Finsler space with infinite series $(\alpha, \beta)$-metric and exponential metric. Next, we deduce an explicit formula for the the $S$-curvature of…

In this paper, we studied a Finsler space whose metric is given by an h-exponential change and obtain the Cartan connection coefficients for the change. We also find the necessary and sufficient condition for an h-exponential change of…

An extension of Riemmann's geometry into a direction dependent geometric structure is usually described by Finsler's geometry. Historically, this construction was motivated by the well-known Riemann's quartic length element example. Quite…

I do not agree with the authors of papers arXiv:0806.2184 and arXiv:0901.1023v1 (published in Phys. Lett., respectively, B668 (2008) 453 and B676 (2009) 173). They consider that \textit{"In Finsler manifold, there exists a unique linear…

We consider the characterization of global attractors $A_f$ for semiflows generated by scalar one-dimensional semilinear parabolic equations of the form $u_t = u_{xx} + f(u,u_x)$, defined on the circle $x\in S^1$, for a class of reversible…

We generalize type $A$ quivers to continuous type $A$ quivers and prove initial results about pointwise finite-dimensional (pwf) representations. We classify the indecomosable pwf representations and provide a decomposition theorem,…

We construct a canonical correspondence from a wide class of reproducing kernels on infinite-dimensional Hermitian vector bundles to linear connections on these bundles. The linear connection in question is obtained through a pull-back…

We study a sequence of connections which is associated with a Riemannian metric and an almost symplectic structure on a manifold. We prove that if this sequence is trivial (i.e. constant) or 2-periodic, then the manifold has a canonical…

This paper investigates the short-time existence and uniqueness of Ricci flow solutions on Finsler manifolds. The main results of this paper are theorems demonstrating the short-time existence of the flow solution for $n$-dimensional…

In the present paper, the $(HM',S,T)$-Cartan connections on pseudo-Finsler manifolds, introduced by A. Bejancu and H.R. Farran, are obtained by the natural almost complex structure arising from the nonlinear connection $HM'$. We prove that…