On Finsler \(\Sigma\)-spaces (Q260343)

The authors study Finsler \(\Sigma\)-spaces. They first prove that any \(\Sigma\)-space is a homogeneous Finsler space. Then, they study some geometric properties of Berwald \(\Sigma\)-spaces and prove that any generalized symmetric Berwald space is a Berwald \(\Sigma\)-space where \(\Sigma\) is cyclic. Then, they show that if each \((1,1)\)-tensor field on a \(\Sigma\)-space is parallel with respect to Berwald connection of a Berwald \(\Sigma\)-space then the space is locally symmetric. Finally, they study some extension theorems and find some important results.