Transverse, type changing, pseudo riemannian metrics and the extendability of geodesics
1994 ◽
Vol 444
(1921)
◽
pp. 297-306
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Keyword(s):
Type I
◽
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.
2007 ◽
Vol 10
(7)
◽
pp. 657-676
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2011 ◽
Vol 31
(3)
◽
pp. 753-756
◽
2010 ◽
Vol 12
(2)
◽
pp. 125-131
2000 ◽
Vol 42
(3-4)
◽
pp. 417-422
◽
2019 ◽
Vol 677
◽
pp. 052066