Differential geometry [electronic resource] / Victor V. Prasolov.

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Differential geometry [electronic resource] / Victor V. Prasolov.

9783030922498 (electronic bk.)
3030922499 (electronic bk.)
3030922480
9783030922481

Cham, Switzerland : Springer, 2022.

English

1 online resource.

10.1007/978-3-030-92249-8 doi

QA641

516.3/6

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.

Includes bibliographical references and index.

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Online resource; title from PDF title page (SpringerLink, viewed February 18, 2022).

Moscow lectures ; v. 8.

Print version: 9783030922481

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