Geodesic
Generalized P-reducible $(\alpha , \beta )$-metrics with vanishing S-curvature
A. Tayebi1 ; H. Sadeghi1
1 Department of Mathematics Faculty of Science University of Qom Qom, Iran
Annales Polonici Mathematici, Tome 114 (2015) no. 1, pp. 67-79.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We study one of the open problems in Finsler geometry presented by Matsumoto–Shimada in 1977, about the existence of a concrete P-reducible metric, i.e. one which is not C-reducible. In order to do this, we study a class of Finsler metrics, called generalized P-reducible metrics, which contains the class of P-reducible metrics. We prove that every generalized P-reducible $(\alpha , \beta )$-metric with vanishing S-curvature reduces to a Berwald metric or a C-reducible metric. It follows that there is no concrete P-reducible $(\alpha ,\beta )$-metric with vanishing S-curvature.
DOI : 10.4064/ap114-1-5
Keywords: study problems finsler geometry presented matsumoto shimada about existence concrete p reducible metric which c reducible order study class finsler metrics called generalized p reducible metrics which contains class p reducible metrics prove every generalized p reducible alpha beta metric vanishing s curvature reduces berwald metric c reducible metric follows there concrete p reducible alpha beta metric vanishing s curvature

A. Tayebi 1 ; H. Sadeghi 1

1 Department of Mathematics Faculty of Science University of Qom Qom, Iran 
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A. Tayebi; H. Sadeghi. Generalized P-reducible $(\alpha , \beta )$-metrics with vanishing S-curvature. Annales Polonici Mathematici, Tome 114 (2015) no. 1, pp. 67-79. doi : 10.4064/ap114-1-5. http://geodesic.mathdoc.fr/articles/10.4064/ap114-1-5/

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