Geodesic
Geodesics on 2-surfaces with pseudo-Riemannian metric: singularities of changes of signature
Sbornik. Mathematics, Tome 200 (2009) no. 3, pp. 385-403

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Smooth 2-surfaces with pseudo-Riemannian metric are considered, that is, ones with quadratic form in the tangent bundle that is not positive-definite. Degeneracy points of the form are said to be parabolic. Geodesic lines induced by this pseudo-Riemannian metric in a neighbourhood of typical parabolic points are considered, their phase portraits are obtained and extremal properties are investigated. Bibliography: 23 titles.
Keywords: pseudo-Riemannian metric, geodesic lines, singular points, resonances, normal forms. 
@article{SM_2009_200_3_a4,
     author = {A. O. Remizov},
     title = {Geodesics on 2-surfaces with {pseudo-Riemannian} metric: singularities of changes of signature},
     journal = {Sbornik. Mathematics},
     pages = {385--403},
     publisher = {mathdoc},
     volume = {200},
     number = {3},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2009_200_3_a4/}
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A. O. Remizov. Geodesics on 2-surfaces with pseudo-Riemannian metric: singularities of changes of signature. Sbornik. Mathematics, Tome 200 (2009) no. 3, pp. 385-403. http://geodesic.mathdoc.fr/item/SM_2009_200_3_a4/