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Introduction to integral geometry in Riemannian homogeneous spaces Takashi Sakai Department of Mathematics and Information Sciences, Tokyo Metropolitan Univer-sity, 1-1 Minami-osawa, Hachioji-shi, Tokyo 192-0397, Japan e-mail: sakai-t@tmu.ac.jp (2010 Mathematics Subject Classi cation: 53C, 53C65.) Abstract. How did Einstein know that Riemannian geometry was necessary for maintaining the equivalence principle in general relativity? Download free software inductive transducers pdf merge.

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This volume is an English translation of Sakai's textbook on Riemannian Geometry which was originally written in Japanese and published in 1992. The author's intent behind the original book was to provide to advanced undergraduate and graudate students an introduction to modern Riemannian geometry that could also serve as a reference. The book begins with an explanation of the fundamental notion of Riemannian geometry. Special emphasis is placed on understandability and readability, to guide students who are new to this area.

The remaining chapters deal with various topics in Riemannian geometry, with the main focus on comparison methods and their applications.

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