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.
作者
田大平
汪敏
TIAN Daping;WANG Min(School of Artificial Intelligence,Jianghan University,Wuhan 430056,Hubei,China)
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
关键词
黎曼流形
散度算子
梯度算子
LAPLACE算子
共形黎曼度量
Riemannian manifolds
divergence operator
gradient operator
Laplacian operator
conformal Riemannian metric