Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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THE TENSION FIELD OF THE ENERGY FUNCTIONAL ON RIEMANNIAN SUBMERSION

  • Received : 2011.02.28
  • Accepted : 2011.05.16
  • Published : 2011.06.30
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Abstract

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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References

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