Differential Geometry
Manifolds, Bundles and Characteristic Classes (Book I-A)
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Beschreibung
This book, Differential Geometry: Manifolds, Bundles and Characteristic Classes (Book I-A), is the first in a captivating series of four books presenting a choice of topics, among fundamental and more advanced, in differential geometry (DG), such as manifolds and tensor calculus, differentiable actions and principal bundles, parallel displacement and exponential mappings, holonomy, complex line bundles and characteristic classes. The inclusion of an appendix on a few elements of algebraic topology provides a didactical guide towards the more advanced Algebraic Topology literature. The subsequent three books of the series are:
Differential Geometry: Riemannian Geometry and Isometric Immersions (Book I-B)
Differential Geometry: Foundations of Cauchy-Riemann and Pseudohermitian Geometry (Book I-C)
Differential Geometry: Advanced Topics in Cauchy–Riemann and Pseudohermitian Geometry (Book I-D)
The four books belong to an ampler book project (Differential Geometry, Partial Differential Equations, and Mathematical Physics, by the same authors) and aim 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, and 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.
This book, Differential Geometry: Manifolds, Bundles and Characteristic Classes (Book I-A), is the first in a captivating series of four books presenting a choice of topics, among fundamental and more advanced, in differential geometry (DG), such as manifolds and tensor calculus, differentiable actions and principal bundles, parallel displacement and exponential mappings, holonomy, complex line bundles and characteristic classes. The inclusion of an appendix on a few elements of algebraic topology provides a didactical guide towards the more advanced Algebraic Topology literature. The subsequent three books of the series are:
Differential Geometry: Riemannian Geometry and Isometric Immersions (Book I-B)
Differential Geometry: Foundations of Cauchy-Riemann and Pseudohermitian Geometry (Book I-C)
Differential Geometry: Advanced Topics in Cauchy–Riemann and Pseudohermitian Geometry (Book I-D)
The four books belong to an ampler book project (Differential Geometry, Partial Differential Equations, and Mathematical Physics, by the same authors) and aim 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, and 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.
Discusses the linear connections: parallel translation, exponential mappings, normal coordinates, and holonomy groups Reviews Sobolev inequalities in the Euclidean setting and how they carry over to Riemannian manifolds Presents the advanced topics in DG: characteristic classes and holonomy theory to the geometry of characteristic classes
Autor*in
Elisabetta Barletta
Themen in »Differential Geometry«
Differentiable Manifold Orbifold Linear Connection Holonomy Group Chern–Weyl Homomorphism Characteristic Class
Stimmen zu »Differential Geometry«
“This textbook is addressed to a wide readership of mathematicians, physicists, students pursuing graduate, masters and higher degrees in mathematics and mathematical physics. … This book provides a lucid and versatile introduction to the methods of differential geometry. … It covers a wealth of important material in a concise, nevertheless instructive manner, and as such it may serve as an excellent guide to further, more advanced and detailed reading in this area of both classical and contemporary mathematics.” (Ahmed Lesfari, zbMATH 1565.53001 2025)
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