Transverse, Type Changing, Pseudo Riemannian Metrics and the Extendability of Geodesics

Details Transverse, Type Changing, Pseudo Riemannian Metrics and the Extendability of Geodesics Transverse, Type Changing, Pseudo Riemannian Metrics and the Extendability of Geodesics

Feb 1994

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994rspsa.444..297k&link_type=abstract

Proceedings: Mathematical and Physical Sciences, Volume 444, Issue 1921, pp. 297-306

Physics

17

Scientific paper

We study the geodesics and pre-geodesics of a smooth manifold with smooth pseudo riemannian metric which changes bilinear type (i.e. the signature changes) on a hypersurface. We classify all geodesics and pre-geodesics that cross the hypersurface of type change transversely. We then apply these results to the eikonal partial differential equation to find geometric conditions for the local existence or non-existence of smooth, transverse solutions.

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