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Regular s-structure on TM. (English) Zbl 0589.53054

The main result of this paper says that any regular s-structure on a Riemannian (or affine) manifold can be ”prolonged” to the corresponding tangent bundle via the complete lifts. In other words, the tangent bundle of a generalized symmetric space is naturally a generalized symmetric space. This is a nontrivial generalization of a known result for symmetric spaces [cf. K. Yano and S. Kobayashi, J. Math. Soc. Japan 18, 194-210 (1966; Zbl 0141.387), and 239-246 (1966; Zbl 0147.215)].
Reviewer: O.Kowalski

MSC:

53C30 Differential geometry of homogeneous manifolds
53C35 Differential geometry of symmetric spaces
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
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