Isospectral hyperbolic surfaces have matching geodesics.
Doyle, Peter G., Rossetti, Juan Pablo (2008)
The New York Journal of Mathematics [electronic only]
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Doyle, Peter G., Rossetti, Juan Pablo (2008)
The New York Journal of Mathematics [electronic only]
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Using Baire categories uniqueness of geodesic segments and existence of closed geodesics on typical convex surfaces are investigated.
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Clairaut’s theorem is expressed on the surfaces of rotation in semi Euclidean 4-space. Moreover, the general equations of time-like geodesic curves are characterized according to the results of Clairaut's theorem on the hyperbolic surfaces of rotation and the elliptic surface of rotation, respectively.
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Annales de la Faculté des sciences de Toulouse : Mathématiques
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