Geodesic
Equimorphisms of Riemannian manifolds
Izvestiya. Mathematics , Tome 6 (1972) no. 3, pp. 518-528.

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We establish a sufficient condition for stability of Riemannian manifolds, i.e. a property according to which every equimorphism of this manifold can be topologically extended to its absolute. 
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     title = {Equimorphisms of {Riemannian} manifolds},
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V. A. Efremovich; È. A. Loginov; E. S. Tikhomirova. Equimorphisms of Riemannian manifolds. Izvestiya. Mathematics , Tome 6 (1972) no. 3, pp. 518-528. http://geodesic.mathdoc.fr/item/IM2_1972_6_3_a4/

[1] Efremovich V., Loginov E., Tikhomirova E., “Ekvimorfizmy rimanovykh mnogoobrazii”, Dokl. AN SSSR, 197:1 (1971), 25–28 | MR | Zbl

[2] Efremovich V., Tikhomirova E., “Ekvimorfizmy giperbolicheskikh prostranstv”, Izv. AN SSSR. Ser. matem., 28 (1964), 1139–1144 | Zbl

[3] Browder W., Levine J., Livesay G. R., “Finding a boundary for an open manifold”, Amer. J. Math., 87:4 (1965), 1017–1028 | DOI | MR | Zbl