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Generalized P-reducible (α,β)-metrics with vanishing S-curvature

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Tayebi A., Sadeghi H.

Annales Polonici Mathematici

2015

tom 114

nr 1

67-79

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 (α,β)-metric with vanishing S-curvature reduces to a Berwald metric or a C-reducible metric. It follows that there is no concrete P-reducible (α,β)-metric with vanishing S-curvature.

Ograniczanie wyników

1 Annales Polonici Mathematici

1 Sadeghi H.

1 Tayebi A.

1 2015

Wyniki wyszukiwania

Generalized P-reducible (α,β)-metrics with vanishing S-curvature