黎曼流形上三个微分算子各自在共形度量下的关系式  

Respective Relational Expression of Three Differential Operators on Riemannian Manifolds Under the Conformal Riemannian Metric

作　　者：田大平 汪敏 TIAN Daping;WANG Min(School of Artificial Intelligence,Jianghan University,Wuhan 430056,Hubei,China)

机构地区：[1]江汉大学人工智能学院,湖北武汉430056

出　　处：《江汉大学学报（自然科学版）》2022年第1期27-32,共6页Journal of Jianghan University：Natural Science Edition

摘　　要：散度算子、梯度算子和Laplace算子不仅是微分几何中非常重要的微分算子,而且在数学的其他分支学科中也扮演着举足轻重的角色。从黎曼几何的角度出发,根据黎曼流形上的散度算子、梯度算子、Laplace算子以及共形的黎曼度量的定义,在黎曼流形的局部坐标系下,通过直接计算,分别推导出散度算子、梯度算子和Laplace算子各自在共形的黎曼度量下的关系式。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.

关 键 词：黎曼流形 散度算子 梯度算子 LAPLACE算子 共形黎曼度量 

分 类 号：O186.1[理学—数学]