The holonomy group of locally projectively flat Randers two-manifolds of constant curvature
نویسندگان
چکیده
منابع مشابه
Projectively Flat Finsler Metrics of Constant Curvature
It is the Hilbert’s Fourth Problem to characterize the (not-necessarilyreversible) distance functions on a bounded convex domain in R such that straight lines are shortest paths. Distance functions induced by a Finsler metric are regarded as smooth ones. Finsler metrics with straight geodesics said to be projective. It is known that the flag curvature of any projective Finsler metric is a scala...
متن کاملRanders Manifolds of Positive Constant Curvature
We prove that any simply connected and complete Riemannian manifold, on which a Randers metric of positive constant flag curvature exists, must be diffeomorphic to an odd-dimensional sphere, provided a certain 1-form vanishes on it. 1. Introduction. The geometry of Finsler manifolds of constant flag curvature is one of the fundamental subjects in Finsler geometry. Akbar-Zadeh [1] proved that, u...
متن کاملPrimitive Compact Flat Manifolds with Holonomy Group
From an important construction of Calabi (see [Ca], [Wo]), it follows that the compact Riemannian flat manifolds with first Betti number zero are the building blocks for all compact Riemannian flat manifolds. It is, therefore, of interest to construct families of such objects. These are often called primitive manifolds. Hantzsche and Wendt (1935) constructed the only existing 3-dimensional comp...
متن کاملOn a class of locally projectively flat Finsler metrics
In this paper we study Finsler metrics with orthogonal invariance. We find a partial differential equation equivalent to these metrics being locally projectively flat. Some applications are given. In particular, we give an explicit construction of a new locally projectively flat Finsler metric of vanishing flag curvature which differs from the Finsler metric given by Berwald in 1929.
متن کاملCharacterization of projective Finsler manifolds of constant curvature having infinite dimensional holonomy group
In this paper we prove that the holonomy group of a simply connected locally projectively flat Finsler manifold of constant curvature is a finite dimensional Lie group if and only if it is flat or it is Riemannian. In particular, the holonomy group of non-Riemannian projective Finsler manifolds of nonzero constant curvature is infinite dimensional.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Differential Geometry and its Applications
سال: 2020
ISSN: 0926-2245
DOI: 10.1016/j.difgeo.2020.101677