Properties on Finsler \(\Sigma\)-spaces (Q6092103)

The authors study Finsler \(\Sigma\)-space, which are a generalization of symmetric spaces. In Theorem 3.5. they prove that such spaces are homogeneous and complete. In Theorem 3.8 they investigate Berwald \(\Sigma\)-spaces and in Theorem 3.13 they prove that for such spaces with scalar flag curvature, if the S-curvature is almost isotropic, then F has constant flag curvature. They prove that a locally projectively flat Finsler space with almost isotropic S-curvature and vanishing flag curvature is Riemannian.