Naturally reductive (α1, α2) metrics
Abstract
Let F be a homogeneous (α1,α2) 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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