A null focal theorem on Lorentz manifolds
Bull. Korean Math. Soc. 2001 Vol. 38, No. 2, 273-284
Jae-Up So
Chonbuk National University
Abstract : Let $P$ be a spacelike $(n-2)$-dimensional submanifold of an $n$-dimensional Lorentz manifold $M$ and let $\sigma$ be a $P$-normal null geodesic with $Ric(\sigma',\, \sigma') \geq m$, for any given nonpositive constant $m$. We establish a sufficient condition such that there is a focal point of $P$ along $\sigma$.
Keywords : Lorentz manifold, null geodesic, focal point, warped product
MSC numbers : 53C50
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