Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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CONVEXITY OF DISTANCE FUNCTION BETWEEN GEODESICS

  • Kim, In-Su (Department of Mathematics and Institute of Pure and Applied Mathematics, Chonbuk University) ;
  • Kim, Yong-Il (School of Liberal Arts & Education, Korea University of Technology and Education) ;
  • Lee, Doo-Hann (School of Liberal Arts & Education, Korea University of Technology and Education)
  • Received : 2008.04.01
  • Accepted : 2008.05.13
  • Published : 2008.06.25
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Abstract

In this paper, we use the convexity of distance function between geodesics in a singular Hadamard space to generalize Hadamard-Cartan theorem for 2-dimensional metric spaces. We also determine a neighborhood of a closed geodesic where no other closed geodesic exists in a complete space of nonpositive curvature.

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References

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