호남수학학술지 (Honam Mathematical Journal)

  • 제36권1호
  • /
  • Pages.141-146
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  • 2014
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  • 1225-293X(pISSN)
  • /
  • 2288-6176(eISSN)
호남수학회 (The Honam Mathematical Society)
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VARIATIONS OF THE LENGTH INTEGRAL

  • Pyo, Yong-Soo (Department of Applied Mathematics, Pukyong National University) ;
  • Oh, Won Tae (Department of Mathematics, Chungbuk National University) ;
  • Son, Heui-Sang (Department of Applied Mathematics, Pukyong National University)
  • 투고 : 2013.12.22
  • 심사 : 2014.01.27
  • 발행 : 2014.03.25
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초록

In this paper, we obtain a necessary and sufficient condition for the second variation of an arbitrarily given smooth variation of a geodesic on a Riemannian manifold to be 0.

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참고문헌

  1. J.-S. Park, Curvature on SU(3)=T (k, l), Kyushu J. Math. 67(1) (2013), 55-65. https://doi.org/10.2206/kyushujm.67.55
  2. Y.-S. Pyo, H.-J. Shin and J.-S. Park, Scalar curvatures on SU(3)=T (k, l), Honam Math. J. 33(4) (2011), 547-556. https://doi.org/10.5831/HMJ.2011.33.4.547
  3. M. Spivak, A Comprehensive Introduction to Di erential Geometry II, Publish or Perish, Inc. Berkeley, 1979.
  4. H. Urakawa, Calculus of Variations and Harmonic Maps (in Japanese), Shokabo Publ., 1990.