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.

引用

页数：14

共 20 条

[1]

[Anonymous], 1986, J. Fac. Sci. Univ. Tokyo Sect. IA Math.

[2]

Beltrami Eugenio, 1865, RISOLUZIONE PROBLEMA

[3]

Burns K, 2006, P AM MATH SOC, V134, P427

[4]

Caponio E, 2011, REV MAT IBEROAM, V27, P919

[5] On the energy functional on Finsler manifolds and applications to stationary spacetimes [J].

Caponio, Erasmo ;

Angel Javaloyes, Miguel ;

Masiello, Antonio .

MATHEMATISCHE ANNALEN, 2011, 351 (02) :365-392

[6] Morse theory of causal geodesics in a stationary spacetime via Morse theory of geodesics of a Finsler metric [J].

Caponio, Erasmo ;

Angel Javaloyes, Miguel ;

Masiello, Antonio .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2010, 27 (03) :857-876

[7]

Lagrange J.-L., 1779, NOVEAUX MEMOIRES ACA, P637

[8]

Levi-Civita T., 1896, Ann. Mat., V24, P255, DOI DOI 10.1007/BF02419530

[9]

Matveev V. S., 2011, P 6 INT M LOR GEOM G

[10]

Matveev V. S., 2004, DOKL AKAD NAUK, V396, P25

← 1 2 →