Abstract
We find all (new) δ-homogeneous invariant Riemannian metrics (including the metrics that are not normal homogeneous) on the spheres of dimensions 4n+3, n ≥ 1, with the greatest Lie group of isometries equal to Sp(n + 1) × U(1) and all homogeneous (non-simply-connected) lens spaces covered by them. All δ-homogeneous Riemannian spaces considered here have positive sectional curvatures and zero Euler characteristic. The answers are found to some previously posed questions.
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Original Russian Text Copyright © 2013 Berestovskiĭ V.N.
The author was partially 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. 5, pp. 972–988, September–October, 2013.
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Berestovskiĭ, V.N. Generalized normal homogeneous spheres S 4n+3 with greatest connected motion group Sp(n + 1) · U(1). Sib Math J 54, 776–789 (2013). https://doi.org/10.1134/S0037446613050029
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DOI: https://doi.org/10.1134/S0037446613050029