论高斯非欧几何学思想的实现途径  

Study on the Approach to Realize the Thought of Gauss' Non-Euclidean Geometry

作　　者：陈惠勇[1] 

机构地区：[1]江西师范大学数学与信息科学学院,南昌330022

出　　处：《自然科学史研究》2011年第2期230-240,共11页Studies in The History of Natural Sciences

基　　金：国家自然科学基金(项目编号:10071085)

摘　　要：将高斯的几何学思想视为一个完整的思想体系,考察高斯的内蕴微分几何学与其非欧几何学思想的深刻内在联系、非欧几何学的实现途径以及实际的大地测量对其非欧几何学思想的验证。认为高斯的内蕴微分几何学本质上已经蕴涵了其非欧几何学的基本思想,并为非欧几何学的发展与最终确认指明了一条微分几何的途径。The thought of Gauss＇ non-Euclidean geometry is intended to reveal that the Euclidean geometry does not have the only physics necessity. Gauss＇ intrinsic differential geometry, however, has deeply revealed the non-Euclidean nature of geometry spaces. This paper studies the inherent relations between Gauss＇ intrinsic differential geometry and non-Euclidean geometry, and the approach to realize his non-Euclidean geometry, and the authentication of his non-Euclidean geometry in his actual geodesy. This paper points out that the thought of Gauss＇ intrinsic differential geometry has pointed out a differential geometry approach of the development and confirmation of non-Euclidean geometry.

关 键 词：高斯 非欧几何学 内蕴微分几何 

分 类 号：O11[理学—数学]