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Generalized normal homogeneous spheres

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Abstract

We find new generalized normal homogeneous but not normal homogeneous Riemannian metrics on spheres of dimensions 4n+3, n ≥ 1, and all homogeneous space forms covered by them; all these spaces have zero Euler characteristic. Deriving consequences, alongside some other new results we obtain new proofs for analogous known results for all complex projective spaces of odd complex dimension starting from three.

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Authors and Affiliations

  1. Omsk Branch of the Sobolev Institute of Mathematics, Omsk, Russia

    V. N. Berestovskiĭ

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  1. V. N. Berestovskiĭ
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Correspondence to V. N. Berestovskiĭ.

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Original Russian Text Copyright © 2013 Berestovskiĭ V.N.

The author was supported by the Russian Foundation for Basic Research (Grant 11-01-00081-a).

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 54, No. 4, pp. 742–761, July–August, 2013.

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Berestovskiĭ, V.N. Generalized normal homogeneous spheres. Sib Math J 54, 588–603 (2013). https://doi.org/10.1134/S0037446613040022

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  • DOI: https://doi.org/10.1134/S0037446613040022

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