RETRACTED ARTICLE: A Family of Finsler Metrics Projectively Related to a Randers Metric
نویسندگان
چکیده
منابع مشابه
On 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.
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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...
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In this paper we study pointwise projectively related Einstein metrics (having the same geodesics as point sets). We show that pointwise projectively related Einstein metrics satisfy a simple equation along geodesics. In particular, we show that if two pointwise projectively related Einstein metrics are complete with negative Einstein constants , then one is a multiple of another.
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ژورنال
عنوان ژورنال: Results in Mathematics
سال: 2012
ISSN: 1422-6383,1420-9012
DOI: 10.1007/s00025-012-0244-z