On the Curvature of the Homogeneous Space U (n+1)/U (n)

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  • On the Curvature of the Homogeneous Spa

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We determine all torsion free invariant affine connections on the homogeneous space S^<2n+1>=U(n+1)/U(n), and characterize their curvatures in terms of the polynomials of their components in the space of curvature-like tensors. The essential difference between the case n=1 and n≥2 is explained in detail from the standpoint of flat affine geometry.

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