Geodesic
Non-existence of closed asymptotic curves on the tubes of negative Gaussian curvature with one-to-one spherical mapping
Fundamentalʹnaâ i prikladnaâ matematika, Tome 1 (1995) no. 4, pp. 953-977.

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It is proved that on the tubes having negative Gaussian curvature and biunique spherical image there is no closed asymptotic curves and by that a Nirenberg's problem is solved which he has posed in relation with the study of rigidity of T-surfaces. 
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G. A. Kovaleva. Non-existence of closed asymptotic curves on the tubes of negative Gaussian curvature with one-to-one spherical mapping. Fundamentalʹnaâ i prikladnaâ matematika, Tome 1 (1995) no. 4, pp. 953-977. http://geodesic.mathdoc.fr/item/FPM_1995_1_4_a7/

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