Geodesics on 2-surfaces with pseudo-Riemannian metric: Singularities of changes of signature. (English. Russian original) Zbl 1169.53318

Remizov, A. O.

Sb. Math. 200, No. 3, 385-403 (2009); translation from Mat. Sb. 200, No. 3, 75-94 (2009).

Summary: 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.

MSC:

53B30	Local differential geometry of Lorentz metrics, indefinite metrics
53C22	Geodesics in global differential geometry
34C20	Transformation and reduction of ordinary differential equations and systems, normal forms