Toomanian, M. Regular s-structure on TM. (English) Zbl 0589.53054 Tensor, New Ser. 42, 225-228 (1985). 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 Cited in 1 ReviewCited in 5 Documents 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.) Keywords:affine manifold; s-structure; tangent bundle; generalized symmetric space Citations:Zbl 0141.387; Zbl 0147.215 PDFBibTeX XMLCite \textit{M. Toomanian}, Tensor, New Ser. 42, 225--228 (1985; Zbl 0589.53054)