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arXiv · 2204.06429

Naturally reductive $(\alpha_1, \alpha_2)$ metrics

Ju Tan·Ming Xu
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Abstract

Let $F$ be a homogeneous $(\alpha_1,\alpha_2)$ metric on the reductive homogeneous manifold $G/H$. Firstly, we characterize the natural reductiveness of $F$ as a local $f$-product between naturally reductive Riemannian metrics. Secondly, 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 when $F$ is naturally reductive.

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Ju Tan, Ming Xu. 2022-04-13. Naturally reductive $(\alpha_1, \alpha_2)$ metrics. https://arxiv.org/abs/2204.06429

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