NATURALLY REDUCTIVE (α1, α2) METRICS∗

doi:10.1007/s10473-023-0406-y

Abstract

Abstract: Letting $F$ be a homogeneous $(\alpha_1,\alpha_2)$ 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.

Key words: (α₁,α₂) metrichomogeneous Finsler space, naturally reductive, S-curvature

Ju TAN, Ming XU. NATURALLY REDUCTIVE (α₁, α₂) METRICS^∗[J].Acta mathematica scientia,Series B, 2023, 43(4): 1547-1560.

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References

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NATURALLY REDUCTIVE (α₁, α₂) METRICS^∗

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