Complete lifts of \(\Sigma\)-spaces. (English) Zbl 0676.53056
\(\Sigma\)-spaces and reduced \(\Sigma\)-spaces were first introduced by O. Loos [Abh. Math. Semin. Univ. Hamb. 37, 160-179 (1972; Zbl 0239.55018)] as generalizations of reflection spaces and symmetric spaces. It is well-known that the tangent bundle to a symmetric space admits a symmetric space structure. In the present paper, the generalization of this result is proved for \(\Sigma\)-spaces (or reduced \(\Sigma\)-spaces, respectively).
Reviewer: O.Kowalski
MSC:
| 53C30 | Differential geometry of homogeneous manifolds |
| 53C20 | Global Riemannian geometry, including pinching |
Citations:
Zbl 0239.55018References:
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