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

A. Tayebi, and H. Sadeghi. "Generalized P-reducible (α,β)-metrics with vanishing S-curvature." Annales Polonici Mathematici 114.1 (2015): 67-79. <http://eudml.org/doc/280991>.

@article{A2015,
abstract = {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.},
author = {A. Tayebi, H. Sadeghi},
journal = {Annales Polonici Mathematici},
keywords = {-reducible metric; -reducible metric; generalized -reducible metric; -metric; -curvature; Landsberg curvature},
language = {eng},
number = {1},
pages = {67-79},
title = {Generalized P-reducible (α,β)-metrics with vanishing S-curvature},
url = {http://eudml.org/doc/280991},
volume = {114},
year = {2015},
}

TY - JOUR
AU - A. Tayebi
AU - H. Sadeghi
TI - Generalized P-reducible (α,β)-metrics with vanishing S-curvature
JO - Annales Polonici Mathematici
PY - 2015
VL - 114
IS - 1
SP - 67
EP - 79
AB - 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.
LA - eng
KW - -reducible metric; -reducible metric; generalized -reducible metric; -metric; -curvature; Landsberg curvature
UR - http://eudml.org/doc/280991
ER -