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WEAKLY SYMMETRIC FINSLER SPACES

SHAOQIANG DENG

School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, P. R. China

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and

ZIXIN HOU

School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, P. R. China

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https://doi.org/10.1142/S0219199710003816Cited by:11 (Source: Crossref)

Abstract

In this paper, we introduce the notion of weakly symmetric Finsler spaces and study some geometrical properties of such spaces. In particular, we prove that each maximal geodesic in a weakly symmetric Finsler space is the orbit of a one-parameter subgroup of the full isometric group. This implies that each weakly symmetric Finsler space has vanishing S-curvature. As an application of these results, we prove that there exist reversible non-Berwaldian Finsler metrics on the 3-dimensional sphere with vanishing S-curvature. This solves an open problem raised by Z. Shen.

Keywords:

AMSC: 22E46, 53C60, 58B20

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