학술저널
THE TENSION FIELD OF THE ENERGY FUNCTIONAL ON RIEMANNIAN SUBMERSION
- 충청수학회
- Journal of the Chungcheong Mathematical Society
- Volume 24, No. 2
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2011.05239 - 245 (7 pages)
- 2
In this paper, we will study the tension ¯eld of the function related to a Riemannain submersion ¼ : N ! M with totally geodesic ¯bres. In case that the Riemannain submersion¼ : N ! M particularly has a smooth map f : M ! N which happens to be a section, we will show that tension ¯eld ¿ (f) of the energy functional can be decomposed into the horizontal and vertical parts.
1. Introduction
2. Riemannian submersion with totally geodesic ¯bres
3. Tension ¯eld of sections
4. Main result
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