Naturally reductive $(\alpha_1, \alpha_2)$ metrics
Differential Geometry
2022-04-14 v1
Abstract
Let be a homogeneous metric on the reductive homogeneous manifold . Firstly, we characterize the natural reductiveness of as a local -product between naturally reductive Riemannian metrics. Secondly, we prove the equivalence among several properties of for its mean Berwald curvature and S-curvature. Finally, we find an explicit flag curvature formula when is naturally reductive.
Cite
@article{arxiv.2204.06429,
title = {Naturally reductive $(\alpha_1, \alpha_2)$ metrics},
author = {Ju Tan and Ming Xu},
journal= {arXiv preprint arXiv:2204.06429},
year = {2022}
}