Letting F be a homogeneous(α_(1),α_(2))metric on the reductive homogeneous manifold G/H,we first characterize the natural reductiveness of F as a local f-product between naturally reductive Riemannian metrics.Second...Letting F be a homogeneous(α_(1),α_(2))metric on the reductive homogeneous manifold G/H,we first characterize the natural reductiveness of F as a local f-product between naturally reductive Riemannian metrics.Second,we prove the equivalence among several properties of F for its mean Berwald curvature and S-curvature.Finally,we find an explicit flag curvature formula for G/H when F is naturally reductive.展开更多
基金the National Natural Science Foundation of China(12131012,12001007,11821101)the Beijing Natural Science Foundation(1222003,Z180004)the Natural Science Foundation of Anhui province(1908085QA03)。
文摘Letting F be a homogeneous(α_(1),α_(2))metric on the reductive homogeneous manifold G/H,we first characterize the natural reductiveness of F as a local f-product between naturally reductive Riemannian metrics.Second,we prove the equivalence among several properties of F for its mean Berwald curvature and S-curvature.Finally,we find an explicit flag curvature formula for G/H when F is naturally reductive.
