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J. Korean Math. Soc. 2003; 40(6): 951-962

Printed November 1, 2003

Copyright © The Korean Mathematical Society.

Focal point in the $C^0$-Lorentzian metric

Jaedong Choi

Air Force Academy

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In this paper we address focal points and treat manifolds $(M,g)$ whose Lorentzian metric tensors $g$ have a spacelike $C^0$-hypersurface $\Sigma$ [10]. We apply Jacobi fields for such manifolds, and check the local length maximizing properties of $C^1$-geodesics. The condition of maximality of timelike curves(geodesics) passing $C^0$-hypersurface is studied.

Keywords: non-smooth Lorentzian metric, focal point

MSC numbers: 53C50, 53B30

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