Projectively flat Finsler 2-spheres 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 کاملGeodesically Reversible Finsler 2-spheres of Constant Curvature
A Finsler space (M,Σ) is said to be geodesically reversible if each oriented geodesic can be reparametrized as a geodesic with the reverse orientation. A reversible Finsler space is geodesically reversible, but the converse need not be true. In this note, building on recent work of LeBrun and Mason [13], it is shown that a geodesically reversible Finsler metric of constant flag curvature on the...
متن کاملar X iv : d g - ga / 9 61 10 10 v 1 2 5 N ov 1 99 6 PROJECTIVELY FLAT FINSLER 2 - SPHERES OF CONSTANT CURVATURE
After recalling the structure equations of Finsler structures on surfaces, I define a notion of ‘generalized Finsler structure’ as a way of micro-localizing the problem of describing Finsler structures subject to curvature conditions. I then recall the basic notions of path geometry on a surface and define a notion of ‘generalized path geometry’ analogous to that of ‘generalized Finsler structu...
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 کاملar X iv : d g - ga / 9 61 10 10 v 1 2 5 N ov 1 99 6 PROJECTIVELY FLAT FINSLER 2 - SPHERES OF CONSTANT
After recalling the structure equations of Finsler structures on surfaces, I define a notion of ‘generalized Finsler structure’ as a way of micro-localizing the problem of describing Finsler structures subject to curvature conditions. I then recall the basic notions of path geometry on a surface and define a notion of ‘generalized path geometry’ analogous to that of ‘generalized Finsler structu...
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ژورنال
عنوان ژورنال: Selecta Mathematica
سال: 1997
ISSN: 1022-1824,1420-9020
DOI: 10.1007/s000290050009