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Differential geometry = Riemannian g...

Barletta, Elisabetta.

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Differential geometry = Riemannian geometry and isometric immersions.. (Book I-B) /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Differential geometry/ by Elisabetta Barletta ... [et al.].
Reminder of title:	Riemannian geometry and isometric immersions.
other author:	Barletta, Elisabetta.
Published:	Singapore :Springer Nature Singapore : : 2025.,
Description:	xvi, 591 p. :ill. (some col.), digital ;24 cm.
[NT 15003449]:	Chapter 1 Riemannian Geometry -- Chapter 2 Finslerian Geometry -- Chapter 3 Isometric immersions.
Contained By:	Springer Nature eBook
Subject:	Geometry, Differential. -
Online resource:	https://doi.org/10.1007/978-981-96-1631-2
ISBN:	9789819616312

Differential geometry = Riemannian geometry and isometric immersions.. (Book I-B) /
Differential geometryRiemannian geometry and isometric immersions.(Book I-B) /[electronic resource] :by Elisabetta Barletta ... [et al.]. - Singapore :Springer Nature Singapore :2025. - xvi, 591 p. :ill. (some col.), digital ;24 cm. - Infosys science foundation series in mathematical sciences,2364-4044. - Infosys science foundation series in mathematical sciences..

Chapter 1 Riemannian Geometry -- Chapter 2 Finslerian Geometry -- Chapter 3 Isometric immersions.

This book, Differential Geometry: Riemannian Geometry and Isometric Immersions (Book I-B), is the second in a captivating series of four books presenting a choice of topics, among fundamental and more advanced in differential geometry (DG). Starting with the basics of semi-Riemannian geometry, the book aims to develop the understanding of smooth 1-parameter variations of geodesics of, and correspondingly of, Jacobi fields. A few algebraic aspects required by the treatment of the Riemann-Christoffel four-tensor and sectional curvature are successively presented. Ricci curvature and Einstein manifolds are briefly discussed. The Sasaki metric on the total space of the tangent bundle over a Riemannian manifold is built, and its main properties are investigated. An important integration technique on a Riemannian manifold, related to the geometry of geodesics, is presented for further applications. The other three books of the series are Differential Geometry 1: Manifolds, Bundle and Characteristic Classes (Book I-A) Differential Geometry 3: Foundations of Cauchy-Riemann and Pseudohermitian Geometry (Book I-C) Differential Geometry 4: Advanced Topics in Cauchy-Riemann and Pseudohermitian Geometry (Book I-D) The four books belong to a larger book project (Differential Geometry, Partial Differential Equations, and Mathematical Physics) by the same authors, aiming to demonstrate how certain portions of DG and the theory of partial differential equations apply to general relativity and (quantum) gravity theory. These books supply some of the ad hoc DG machinery yet do not constitute a comprehensive treatise on DG, but rather authors' choice based on their scientific (mathematical and physical) interests. These are centered around the theory of immersions-isometric, holomorphic, Cauchy-Riemann (CR)-and pseudohermitian geometry, as devised by Sidney Martin Webster for the study of nondegenerate CR structures, themselves a DG manifestation of the tangential CR equations.

ISBN: 9789819616312

Standard No.: 10.1007/978-981-96-1631-2doiSubjects--Topical Terms:

523835
Geometry, Differential.

LC Class. No.: QA641

Dewey Class. No.: 516.36

Differential geometry = Riemannian geometry and isometric immersions.. (Book I-B) /
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490 1 $a Infosys science foundation series in mathematical sciences, $x 2364-4044
505 0 $a Chapter 1 Riemannian Geometry -- Chapter 2 Finslerian Geometry -- Chapter 3 Isometric immersions.
520 $a This book, Differential Geometry: Riemannian Geometry and Isometric Immersions (Book I-B), is the second in a captivating series of four books presenting a choice of topics, among fundamental and more advanced in differential geometry (DG). Starting with the basics of semi-Riemannian geometry, the book aims to develop the understanding of smooth 1-parameter variations of geodesics of, and correspondingly of, Jacobi fields. A few algebraic aspects required by the treatment of the Riemann-Christoffel four-tensor and sectional curvature are successively presented. Ricci curvature and Einstein manifolds are briefly discussed. The Sasaki metric on the total space of the tangent bundle over a Riemannian manifold is built, and its main properties are investigated. An important integration technique on a Riemannian manifold, related to the geometry of geodesics, is presented for further applications. The other three books of the series are Differential Geometry 1: Manifolds, Bundle and Characteristic Classes (Book I-A) Differential Geometry 3: Foundations of Cauchy-Riemann and Pseudohermitian Geometry (Book I-C) Differential Geometry 4: Advanced Topics in Cauchy-Riemann and Pseudohermitian Geometry (Book I-D) The four books belong to a larger book project (Differential Geometry, Partial Differential Equations, and Mathematical Physics) by the same authors, aiming to demonstrate how certain portions of DG and the theory of partial differential equations apply to general relativity and (quantum) gravity theory. These books supply some of the ad hoc DG machinery yet do not constitute a comprehensive treatise on DG, but rather authors' choice based on their scientific (mathematical and physical) interests. These are centered around the theory of immersions-isometric, holomorphic, Cauchy-Riemann (CR)-and pseudohermitian geometry, as devised by Sidney Martin Webster for the study of nondegenerate CR structures, themselves a DG manifestation of the tangential CR equations.
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