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 Riemanuian manifold. This unifies the known results and simplifies the co...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 Riemanuian 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.展开更多
文摘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 Riemanuian 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.
