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Remizov, A. O.; Tari, F.

Singularities of the geodesic flow on surfaces with pseudo-Riemannian metrics. (English) Zbl 1353.53050

Geom. Dedicata 185, 131-153 (2016).
Summary: We consider a pseudo-Riemannian metric that changes signature along a smooth curve on a surface, called the discriminant curve. The discriminant curve separates the surface locally into a Riemannian and a Lorentzian domain. We study the local behaviour and properties of geodesics at a point on the discriminant where the isotropic direction is tangent to the discriminant curve.

Cited in 7 Documents

MSC:

53C22 Geodesics in global differential geometry
53B30 Local differential geometry of Lorentz metrics, indefinite metrics
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
53D25 Geodesic flows in symplectic geometry and contact geometry

Keywords:

pseudo-Riemannian metrics; geodesics; singular points; normal forms
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References:

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