Geodesic
Oval lines of the hyperbolic plane of positive curvature
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 12 (2012) no. 3, pp. 37-44

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The classification of real nondegenerate second-order lines of the hyperbolic plane $\hat H$ of positive curvature is obtained. It is proved that the basic geometric covariants and the property of line to be convex (nonconvex) determine seven types of intrinsic oval lines and eight types of nonintrinsic oval line on $\hat H$. For every intrinsic oval lines the associate projective frame is constructed and the canonical equation is received. 
@article{ISU_2012_12_3_a5,
     author = {L. N. Romakina},
     title = {Oval lines of the hyperbolic plane of positive curvature},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
     pages = {37--44},
     publisher = {mathdoc},
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     number = {3},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ISU_2012_12_3_a5/}
}
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L. N. Romakina. Oval lines of the hyperbolic plane of positive curvature. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 12 (2012) no. 3, pp. 37-44. http://geodesic.mathdoc.fr/item/ISU_2012_12_3_a5/