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Differential geometry [electronic resource]
- 作者： Prasolov, Victor V.
- 其他作者：
- 其他題名：
- Moscow lectures ;
- 出版： Cham : Springer International Publishing :Imprint: Springer
- 叢書名： Moscow lectures,v. 8
- 主題： Geometry, Differential. , Differential Geometry.
- ISBN： 9783030922498 (electronic bk.) 、 9783030922481 (paper)
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FIND@SFXID:
CGU
- 資料類型: 電子書
- 內容註: Curves in the Plane -- Curves in Space -- Surfaces in Space -- Hypersurfaces in Rn+1 -- Connections -- Riemannian Manifolds -- Lie Groups -- Comparison Theorems -- Curvature and Topology -- Laplacian -- Appendix -- Bibliography -- Index.
- 摘要註: This book combines the classical and contemporary approaches to differential geometry. An introduction to the Riemannian geometry of manifolds is preceded by a detailed discussion of properties of curves and surfaces. The chapter on the differential geometry of plane curves considers local and global properties of curves, evolutes and involutes, and affine and projective differential geometry. Various approaches to Gaussian curvature for surfaces are discussed. The curvature tensor, conjugate points, and the Laplace-Beltrami operator are first considered in detail for two-dimensional surfaces, which facilitates studying them in the many-dimensional case. A separate chapter is devoted to the differential geometry of Lie groups.
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讀者標籤：
- 系統號： 005513349 | 機讀編目格式
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