충청수학회지 (Journal of the Chungcheong Mathematical Society)

  • 제24권2호
  • /
  • Pages.239-245
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  • 2011
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  • 1226-3524(pISSN)
  • /
  • 2383-6245(eISSN)
충청수학회 (The Chungcheong Mathematical Society)
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THE TENSION FIELD OF THE ENERGY FUNCTIONAL ON RIEMANNIAN SUBMERSION

  • 투고 : 2011.02.28
  • 심사 : 2011.05.16
  • 발행 : 2011.06.30
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초록

In this paper, we will study the tension field of the function related to a Riemannain submersion ${\pi}\;:\;N{\rightarrow}M$ with totally geodesic fibres. In case that the Riemannain submersion ${\pi}\;:\;N{\rightarrow}M$ particularly has a smooth map $f\;:\;M{\rightarrow}N$ which happens to be a section, we will show that tension field ${\tau}(f)$ of the energy functional can be decomposed into the horizontal and vertical parts.

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참고문헌

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  5. B. O'Neill, The fundamental equations of a submersion, Michigan Math. J. 13 (1966), 459-469. https://doi.org/10.1307/mmj/1028999604