Abstract
A two-parameter family of invariant almost-complex structures J α,c is given on the homogeneous space M × M’ = U(n + 1)/U(n) × U(p + 1)/U(p); all these structures are integrable. We consider all invariant Riemannian metrics on the homogeneous space M × M’. They depend on five parameters and are Hermitian with respect to some complex structure J α,c . In this paper, we calculate the Ricci tensor, scalar curvature, and obtain estimates of the sectional curvature for any metric on M × M’. All the invariant metrics of nonnegative curvature are described. We obtain the extremal values of the scalar curvature functional on the four-parameter family of metrics g α,c,λ,λ’;1 .
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Daurtseva, N.A. U(n + 1) × U(p + 1)-Hermitian metrics on the manifold S 2n+1 × S 2p+1 . Math Notes 82, 180–195 (2007). https://doi.org/10.1134/S0001434607070231
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DOI: https://doi.org/10.1134/S0001434607070231