文摘

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.