关键词: 黎曼流形, 散度算子, 梯度算子, Laplace 算子, 共形黎曼度量

Abstract: Divergence operators， gradient operators and Laplacian operators are critical differential operators in differential geometry and play an essential role in other branches of mathematics. In this paper，from the perspective of Riemannian geometry，according to the definitions of the divergence operator， gradient operator， Laplacian operator and the conformal Riemannian metric on Riemannian manifolds，in the local coordinate system of Riemannian manifolds，we derive the relational expressions of the divergence operator，gradient operator and Laplacian operator under the conformal Riemannian metric respectively through direct calculations.

Key words: Riemannian manifolds, divergence operator, gradient operator, Laplacian operator, conformal Riemannian metric