Geodesic
Eigenfunctions of the Beltrami--Laplace operator on a hyperboloid of one sheet
Matematičeskie zametki, Tome 7 (1970) no. 2, pp. 255-263.

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The Beltrami–Laplace operator $\Delta$ on a one-sheeted hyperboloid is hyperbolic. There is taken the set of functions bounded outside some neighborhood of two isotropic lines, intersecting at infinity. A necessary and sufficient condition is derived that a function of this set be an eigenfunction of the operator $\Delta$. 
@article{MZM_1970_7_2_a14,
     author = {V.-B. K. Rogov},
     title = {Eigenfunctions of the {Beltrami--Laplace} operator on a hyperboloid of one sheet},
     journal = {Matemati\v{c}eskie zametki},
     pages = {255--263},
     publisher = {mathdoc},
     volume = {7},
     number = {2},
     year = {1970},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1970_7_2_a14/}
}
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V.-B. K. Rogov. Eigenfunctions of the Beltrami--Laplace operator on a hyperboloid of one sheet. Matematičeskie zametki, Tome 7 (1970) no. 2, pp. 255-263. http://geodesic.mathdoc.fr/item/MZM_1970_7_2_a14/