Geodesic
Jacobi Fields along a Geodesic with Random Curvature
Matematičeskie zametki, Tome 74 (2003) no. 3, pp. 416-424.

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A notion of a renewable geodesic on which the curvature is a random process is introduced. It is shown that the modulus of the Jacobi field along such a geodesic grows exponentially. At the same time, the existence with probability 1 of infinitely many conjugate points is demonstrated. 
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V. G. Lamburt; D. D. Sokolov; V. N. Tutubalin. Jacobi Fields along a Geodesic with Random Curvature. Matematičeskie zametki, Tome 74 (2003) no. 3, pp. 416-424. http://geodesic.mathdoc.fr/item/MZM_2003_74_3_a9/

[1] Gromol D., Klingenberg V., Meier V., Rimanova geometriya v tselom, Mir, M., 1971

[2] Aleksandrov A. D., Vnutrennyaya geometriya vypuklykh poverkhnostei, OGIZ, M.–L., 1948 | Zbl

[3] Pogorelov A. V., Vneshnyaya geometriya vypuklykh poverkhnostei, Nauka, M., 1975 | Zbl

[4] Gilbert D., Osnovaniya geometrii, OGIZ, M.–L., 1948

[5] Efimov N. V., “Vozniknovenie osobennostei na poverkhnostyakh otritsatelnoi krivizny”, Matem. sb., 64(106):2 (1964), 286–320 | MR | Zbl

[6] Efimov N. V., “Giperbolicheskie zadachi teorii poverkhnostei.”, Trudy mezhdunarodnogo kongressa matematikov (Moskva, 1966), Mir, M., 1968, 177–188 | MR

[7] Bakelman I. Ya., Verner A. L., Kantor B. E., Vvedenie v differentsialnuyu geometriyu “v tselom”, Nauka, M., 1973 | Zbl

[8] Furstenberg H. A, “Poisson formula for semi-simple Lie groups”, Ann. Math., 77:2 (1963), 335–386 | DOI | MR | Zbl

[9] Furstenberg H., “Noncommuting random products”, Trans. Amer. Math. Soc., 108:3 (1963), 377–428 | DOI | MR | Zbl