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中 文 摘 要
黎曼是十九世纪最伟大的数学家之一,他的一生十分短暂,但对科学的贡献却是不容忽视的。他在微分几何方面取得了重大突破,创建了黎曼几何,这对整个几何学的发展起到了巨大的推动作用。令人赞叹的是,这一个多世纪前的成就几乎直接同现代数学中的拓扑方法、一般流形概念、代数几何学等紧密相连,他和他的接班人——贝尔特拉米、克里斯托费尔、李普希茨所发展的微分张量分析逐渐成为研究流形上几何结构和分析的一个重要工具。他的空间观念及黎曼几何更预示着广义相对论的诞生,正是他触发了现代数学的革命性变革,并激发起后人对此的研究及拓展。
学科间并非孤立的,人们需要全面辩证地考虑它们之间的关系。本文在分析黎曼的几何思想的基础上,着重论述了它对数学和物理学两个领域所产生的深远影响。

关键词:黎曼 几何思想 张量分析 相对论

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The 黎曼 is one of the greatest mathematicians of 19 centuries, his whole life is very brief, but to the contribution of science is to allow of no something to neglect.He is several in the differential calculus the aspect obtained the graveness breakthrough, established the 黎曼 several, this whole geometry of development rise arrived the huge push function.Highly praised is, this have another century ago of achievement almost and directly and together the 拓 within modern mathematics rushed toward the method and flowed the form concept, the algebra geometry...etc. generally close connect with each other, he pulled the rice, gram with his successor- shell 尔 especially in the 斯 gave the fee 尔 , LI3 PU3 XI 茨 develop of differential calculus ZHANG LIANG2 the analysis became the research to flow the form gradually up several structure and analytical important tools.His space idea and severals of the 黎曼 even indicate the naissance of the general theory of Relativity, exactly he triggered the modern the revolution of mathematics change, and stir up rise posterity to this research and expand.
The course stands alone not of, the people need the overall dialectical ground relation that considers them.This text foundation thought in several of the analytical 黎曼 up, emphasized to discuss its logarithms to learn and profound influence that two realm of physics produce.

Chinese language to be picked
Liman is one of the 19th century's greatest mathematician, and his very short life, but the contribution of science can not be overlooked. He differential geometric achieved a major breakthrough in the establishment of Limanjihe, for the entire geometry has played a tremendous role in promoting the development. Remarkable is that this more than a century ago almost directly with the achievement of modern mathematics, the following methods, the general flow is concepts, algebra to geometry closely linked, he and his successors -- Beiertelami, Christopher Tuofeier, Lee Puxici developed differential Zhang volume analysis has gradually become more research on the flow geometry and analysis of an important tool. His concept of space and relativity Limanjihe more herald the birth of modern mathematics is triggered his revolutionary change, and stimulate people to the research and development. Interdisciplinary not isolated, people need to consider their full dialectical relationship. The geometric thinking in the analysis Liman, on the basis of mathematics and physics it focuses on the two areas of the far-reaching implications.
Keyword : Liman geometric analysis of the theory of relativity and Zhang