Complete Formulas for the Volumes of Tubes about Curves in a Riemannian Manifold |
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| Authors: | Fa En Wu |
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| Institution: | (1) Department of Mathematics, Northern Jiaotong University, Beijing 100044, P. R. China, E-mail: fewu@center.njtu.edu.cn, CN |
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| Abstract: | By using the Taylor expansions of the solutions of Jacobi equations, we obtain the complete formulas for the volumes of tubes
about curves in a Riemannian manifold. This unifies the known results and simplifies the computations involved in this direction.
In the special case of surfaces, we also obtain the corresponding complete formulas which generalize the known results.
Received July 23, 1998, Accepted January 14, 1999 |
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| Keywords: | Fermi coordinates N-Jacobi field Taylor expansion Volumes of tubes |
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