Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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A NULL FOCAL THEOREM ON LORENTZ MANIFOLDS

  • So, Jae-Up (DEPARTMENT OF MATHEMATICS, CHONBUK NATIONAL UNIVERSITY)
  • Published : 2001.05.01
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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 the any given nonpositive constant m. We establish a sufficient condition such that there is a focal point of P along $\sigma$.

Keywords

References

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  2. Comm. Pure Appl. Math. v.34 A lower bound for the heat kernel J. Cheeger;S. T. Yau.
  3. Ann. Sci. Ecole Norm. Sup. v.11 A general comparison theorem with application to volume estimates for submanifolds E. Heintze;H. Karcher