内蒙古民族大学学报（自然科学版）2025，Vol.40Issue(3)：77-83,7.DOI:10.14045/j.cnki.15-1220.2025.03.011
4维球面上的测地线
Geodesics on A 4-dimensional Sphere
摘要
Abstract
The research on the unit sphere S2 and S3 is relatively mature.In order to obtain the geodesic on the unit 4-sphereS4,S2 and S3 are studied.The geodesic polar coordinates of S2 and S3 are extended to S4.Through the study and analysis of S4,a new frame on the unit 4-sphere S4 is obtained and the Riemannian metric g is defined.At the same time,the coefficient of Levi-Civita connection of Riemannian manifold(S4,g)is calculated,and the equation of geodesic on Riemannian manifold(S4,g)is obtained.关键词
4维球面/黎曼度量/Levi-Civita联络/测地线Key words
4-dimensional sphere/Riemannian metric/Levi-Civita connection/geodesics分类
数理科学引用本文复制引用
罗学民,包图雅,刘秀雨..4维球面上的测地线[J].内蒙古民族大学学报（自然科学版）,2025,40(3):77-83,7.基金项目
国家自然科学基金项目(11561062) （11561062）
内蒙古自治区自然科学基金项目(2022MS01015) （2022MS01015）
