Geodesic
Bertrand surfaces with a pseudo-Riemannian metric of revolution
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2015), pp. 66-69

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A generalization of the classic Bertrand theorem to surfaces of revolution with an indefinite metric without equators is presented. Their embeddings into the Minkowski space $\mathbb{R}^3_2$ are constructed and an analogue of Santoprete's criterion is formulated. 
@article{VMUMM_2015_1_a13,
     author = {O. A. Zagryadskii},
     title = {Bertrand surfaces with a {pseudo-Riemannian} metric of revolution},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {66--69},
     publisher = {mathdoc},
     number = {1},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2015_1_a13/}
}
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O. A. Zagryadskii. Bertrand surfaces with a pseudo-Riemannian metric of revolution. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2015), pp. 66-69. http://geodesic.mathdoc.fr/item/VMUMM_2015_1_a13/