Geodesic
Geodesic uniqueness in the whole of some generally recurrent Riemannian spaces
Fundamentalʹnaâ i prikladnaâ matematika, Tome 16 (2010) no. 2, pp. 93-101 
H. N. Sinyukova. Geodesic uniqueness in the whole of some generally recurrent Riemannian spaces. Fundamentalʹnaâ i prikladnaâ matematika, Tome 16 (2010) no. 2, pp. 93-101. http://geodesic.mathdoc.fr/item/FPM_2010_16_2_a9/
@article{FPM_2010_16_2_a9,
     author = {H. N. Sinyukova},
     title = {Geodesic uniqueness in the whole of some generally recurrent {Riemannian} spaces},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {93--101},
     year = {2010},
     volume = {16},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2010_16_2_a9/}
}
TY  - JOUR
AU  - H. N. Sinyukova
TI  - Geodesic uniqueness in the whole of some generally recurrent Riemannian spaces
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2010
SP  - 93
EP  - 101
VL  - 16
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/FPM_2010_16_2_a9/
LA  - ru
ID  - FPM_2010_16_2_a9
ER  - 
%0 Journal Article
%A H. N. Sinyukova
%T Geodesic uniqueness in the whole of some generally recurrent Riemannian spaces
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2010
%P 93-101
%V 16
%N 2
%U http://geodesic.mathdoc.fr/item/FPM_2010_16_2_a9/
%G ru
%F FPM_2010_16_2_a9

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we present a detailed proofs of two theorems of geodesic uniqueness in the whole of compact, in some sense generally recurrent, Riemannian spaces with a positive defined metric. Our studies are based on the H. Hopf theorem.

[1] Kobayasi Sh., Nomidzu K., Osnovy differentsialnoi geometrii, v. 1, Nauka, M., 1981

[2] Sinyukov N. S., Geodezicheskie otobrazheniya rimanovykh prostranstv, Nauka, M., 1979 | MR | Zbl

[3] Sinyukova E. N., “O geodezicheskikh otobrazheniyakh nekotorykh spetsialnykh rimanovykh prostranstv”, Mat. zametki, 30:6 (1981), 889–894 | MR | Zbl

[4] Stepanov S. E., “Teoremy ischeznoveniya v affinnoi, rimanovoi i lorentsevoi geometriyakh”, Fundament. i prikl. mat., 11:1 (2005), 35–84 | MR | Zbl

[5] Eizenkhart L. P., Rimanova geometriya, IL, M., 1948

[6] Yano K., Bokhner S., Krivizna i chisla Betti, IL, M., 1957 | MR

[7] Vránceanu G., “Proprietáti globale ale spaliilor bui Riemann cu conexiane abina constanta”, Stud. Cerc. Mat., 14:1 (1963), 7–22 | MR | Zbl