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Geodesic and holomorphically projective mappings of $$m$$-pseudo- and $$m$$-quasisymmetric Riemannian spaces. (English. Russian original) Zbl 0890.53041
Russ. Math. 40, No. 10, 28-32 (1996); translation from Izv. Vyssh. Uchebn., Mat 1996, No. 10(413), 30-35 (1996).
This article is a generalisation of two results of the Ph. D. thesis of the first author. The $$m$$-pseudo space and $$m$$-quasisymmetric space are generalisations of semisymmetric, $$m$$-symmetric pseudosymmetric (generalized semisymmetric) and quasisymmetric spaces. Considering the geodesics in Riemannian space, the authors define a special class of Riemannian spaces and prove that these spaces are closed with respect to geodesic mappings. The same result is proved for Kähler spaces.
Reviewer: S.Noaghi (Vulcan)

##### MSC:
 53C22 Geodesics in global differential geometry 53C35 Differential geometry of symmetric spaces 53C55 Global differential geometry of Hermitian and Kählerian manifolds
##### Keywords:
quasisymmetric spaces; semisymmetric spaces