ON PROJECTIVE EQUIVALENCE AND POINTWISE PROJECTIVE RELATION OF RANDERS METRICS

被引：10
|
作者：
Matveev, Vladimir S. [1 ]
机构：
[1] Univ Jena, Inst Math, D-07737 Jena, Germany
来源：
INTERNATIONAL JOURNAL OF MATHEMATICS | 2012年 / 23卷 / 09期
关键词：
Finsler metrics; Randers metrics; projective equivalence; pointwise projective relation; projective transformations; LICHNEROWICZ-OBATA CONJECTURE;
D O I：
10.1142/S0129167X12500930
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We prove that projective equivalence of two Randers Finsler metrics F = root g(xi, xi) + omega(xi) and (F) over bar = root(g) over bar(xi, xi) + (omega) over bar(xi) such that at least one of the one-forms omega and (omega) over bar is not closed implies that for a certain constant C > 0 we have g = C-2 . (g) over bar and the form omega-C . (omega) over bar is closed. As an application we prove the natural generalization of the projective Lichnerowicz-Obata conjecture for Randers metrics.
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页数：14
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