Completion of the classification of generic singularities of geodesic

N. G. Pavlova ; A. O. Remizov

Izvestiya. Mathematics , Tome 83 (2019) no. 1, pp. 104-123.

Résumé

This is the final paper in a series devoted to generic singularities of geodesic flows for two-dimensional pseudo-Riemannian metrics of changing signature and metrics induced from the Euclidean metric of the ambient space on surfaces with a cuspidal edge. We study the local phase portraits and the properties of geodesics at degenerate points of a certain type. This completes the list of singularities in codimensions $1$ and $2$.

Détail

Keywords: pseudo-Riemannian metric, geodesic, singular point, normal form, invariant manifold.

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