相关论文: Affinely rigid Finsler manifolds
In this work we show that for the geodesic spray $S$ of a Finsler function $F$ the most natural projective deformation $\widetilde{S}=S -2 \lambda F\mathbb C$ leads to a non-Finsler metrizable spray, for almost every value of $\lambda \in…
In this paper we characterize sprays that are metrizable by Finsler functions of constant flag curvature. By solving a particular case of the Finsler metrizability problem we provide the necessary and sufficient conditions that can be used…
The projective metrizability problem can be formulated as follows: under what conditions the geodesics of a given spray coincide with the geodesics of some Finsler space, as oriented curves. In Theorem 3.8 we reformulate the projective…
It is well known that a system of homogeneous second-order ordinary differential equations (spray) is necessarily isotropic in order to be metrizable by a Finsler function of scalar flag curvature. In Theorem 3.1 we show that the isotropy…
In this paper we study the invariant metrizability and projective metrizability problems for the special case of the geodesic spray associated to the canonical connection of a Lie group. We prove that such canonical spray is projectively…
We prove that a locally integrable function $f:(a,b) \to \mathbb R$ must be affine if its mean oscillation, considered as a function of intervals, can be extended to a locally finite Borel measure. In particular, we show that any function…
Every Finsler metric naturally induces a spray but not so for the converse. The notion for sprays of scalar (resp. isotropic) curvature has been known as a generalization for Finsler metrics of scalar (resp. isotropic) flag curvature. In…
In the previous work, the notion of the Finsleroid--Finsler space have been formulated and the necessary and sufficient conditions for the space to be of the Landsberg type have been found. In the present paper, starting with particular…
In this paper, we consider projective deformation of the geodesic system of Finsler spaces by holonomy invariant functions: Starting by a Finsler spray $S$ and a holonomy invariant function $P$, we investigate the metrizability property of…
We study a special class of Finsler metrics which we refer to as Almost Rational Finsler metrics (shortly, AR-Finsler metrics). We give necessary and sufficient conditions for an AR-Finsler manifold $(M,F)$ to be Riemannian. The rationality…
A function $f:\RR \to \RR$ is called \emph{vertically rigid} if $graph(cf)$ is isometric to $graph (f)$ for all $c \neq 0$. We prove Jankovi\'c's conjecture by showing that a continuous function is vertically rigid if and only if it is of…
In this paper, we consider a left invariant complex Finsler metric $F$ on a complex Lie group. Using the technique of invariant frames, we prove the following properties for $(G,F)$. First, the metric $F$ must be a complex Berwald metric.…
Hamel functions of a spray play an important role in the study of the projective metrizability of the concerned spray, and Funk functions are special Hamel functions. A Finsler metric is a special Hamel function of the spray induced by the…
In this paper, we prove a global rigidity theorem for negatively curved Finsler metrics on a compact manifold of dimension n>2. We show that for such a Finsler manifold, if the flag curvature is a scalar function on the tangent bundle, then…
In this paper we investigate aspects of rigidity and flexibility for conformal iterated function systems. For the case in which the systems are not essentially affine we show that two such systems are conformal equivalent if and only if in…
Locally projectively flat metrics (or sprays) form a rich class of metrics (or sprays) in Finsler and spray geometry. The characterization of such metrics is the Hilbert Fourth Problem in the regular case. In this paper we study the…
We show that monochromatic Finsler metrics, i.e., Finsler metrics such that each two tangent spaces are isomorphic as normed spaces, are generalized Berwald metrics, i.e., there exists an affine connection, possibly with torsion, that…
A function $f:\RR^n \to \RR$ is called \emph{vertically rigid} if $graph(cf)$ is isometric to $graph (f)$ for all $c \neq 0$. We settled Jankovi\'c's conjecture in a separate paper by showing that a continuous function $f:\RR \to \RR$ is…
For a standard Finsler metric F on a manifold M, its domain is the whole tangent bundle TM and its fundamental tensor g is positive-definite. However, in many cases (for example, the well-known Kropina and Matsumoto metrics), these two…
For a $2$-dimensional non-flat spray we associate a Berwald frame and a $3$-dimensional distribution that we call the Berwald distribution. The Frobenius integrability of the Berwald distribution characterises the Finsler metrizability of…