An Introduction To Infinite Dimensional Differential Geometry
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Author | : Alexander Schmeding |
Publisher | : Cambridge University Press |
Total Pages | : 284 |
Release | : 2022-12-22 |
Genre | : Mathematics |
ISBN | : 1009089307 |
Introducing foundational concepts in infinite-dimensional differential geometry beyond Banach manifolds, this text is based on Bastiani calculus. It focuses on two main areas of infinite-dimensional geometry: infinite-dimensional Lie groups and weak Riemannian geometry, exploring their connections to manifolds of (smooth) mappings. Topics covered include diffeomorphism groups, loop groups and Riemannian metrics for shape analysis. Numerous examples highlight both surprising connections between finite- and infinite-dimensional geometry, and challenges occurring solely in infinite dimensions. The geometric techniques developed are then showcased in modern applications of geometry such as geometric hydrodynamics, higher geometry in the guise of Lie groupoids, and rough path theory. With plentiful exercises, some with solutions, and worked examples, this will be indispensable for graduate students and researchers working at the intersection of functional analysis, non-linear differential equations and differential geometry. This title is also available as Open Access on Cambridge Core.
Author | : Alexander Schmeding |
Publisher | : Cambridge University Press |
Total Pages | : 283 |
Release | : 2022-12-31 |
Genre | : Mathematics |
ISBN | : 1316514889 |
Introduces foundational concepts in infinite-dimensional differential geometry beyond Banach manifolds, showcasing its modern applications.
Author | : Serge Lang |
Publisher | : Springer Science & Business Media |
Total Pages | : 553 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461205417 |
This book provides an introduction to the basic concepts in differential topology, differential geometry, and differential equations, and some of the main basic theorems in all three areas. This new edition includes new chapters, sections, examples, and exercises. From the reviews: "There are many books on the fundamentals of differential geometry, but this one is quite exceptional; this is not surprising for those who know Serge Lang's books." --EMS NEWSLETTER
Author | : J.K. Hale |
Publisher | : Springer Science & Business Media |
Total Pages | : 203 |
Release | : 2013-04-17 |
Genre | : Mathematics |
ISBN | : 1475744935 |
Including: An Introduction to the Homotopy Theory in Noncompact Spaces
Author | : Andreas Kriegl |
Publisher | : American Mathematical Soc. |
Total Pages | : 631 |
Release | : 1997 |
Genre | : Mathematics |
ISBN | : 0821807803 |
For graduate students and research mathematicians interested in global analysis and the analysis of manifolds, lays the foundations for a differential calculus in infinite dimensions and discusses applications in infinite-dimension differential geometry and global analysis not involving Sobolev completions and fixed-point theory. Shows how the notion of smoothness as mapping smooth curves to smooth curves coincides with all known reasonable concepts up to Frechet spaces. Then develops a calculus of holomorphic mappings, and another of real analytical mapping. Emphasizes regular infinite dimensional Lie groups. Annotation copyrighted by Book News, Inc., Portland, OR
Author | : Serge Lang |
Publisher | : Springer |
Total Pages | : 250 |
Release | : 2010-12-03 |
Genre | : Mathematics |
ISBN | : 9781441930194 |
Author is well-known and established book author (all Serge Lang books are now published by Springer); Presents a brief introduction to the subject; All manifolds are assumed finite dimensional in order not to frighten some readers; Complete proofs are given; Use of manifolds cuts across disciplines and includes physics, engineering and economics
Author | : J. Madore |
Publisher | : Cambridge University Press |
Total Pages | : 381 |
Release | : 1999-06-24 |
Genre | : Mathematics |
ISBN | : 0521659914 |
A thoroughly revised introduction to non-commutative geometry.
Author | : Serge Lang |
Publisher | : |
Total Pages | : 564 |
Release | : 1998-12-01 |
Genre | : |
ISBN | : 9781461205425 |
Author | : Jack K. Hale |
Publisher | : Springer Science & Business Media |
Total Pages | : 287 |
Release | : 2002-07-12 |
Genre | : Mathematics |
ISBN | : 0387954635 |
State-of-the-art in qualitative theory of functional differential equations; Most of the new material has never appeared in book form and some not even in papers; Second edition updated with new topics and results; Methods discussed will apply to other equations and applications
Author | : Joel W. Robbin |
Publisher | : Springer Nature |
Total Pages | : 426 |
Release | : 2022-01-12 |
Genre | : Mathematics |
ISBN | : 3662643405 |
This textbook is suitable for a one semester lecture course on differential geometry for students of mathematics or STEM disciplines with a working knowledge of analysis, linear algebra, complex analysis, and point set topology. The book treats the subject both from an extrinsic and an intrinsic view point. The first chapters give a historical overview of the field and contain an introduction to basic concepts such as manifolds and smooth maps, vector fields and flows, and Lie groups, leading up to the theorem of Frobenius. Subsequent chapters deal with the Levi-Civita connection, geodesics, the Riemann curvature tensor, a proof of the Cartan-Ambrose-Hicks theorem, as well as applications to flat spaces, symmetric spaces, and constant curvature manifolds. Also included are sections about manifolds with nonpositive sectional curvature, the Ricci tensor, the scalar curvature, and the Weyl tensor. An additional chapter goes beyond the scope of a one semester lecture course and deals with subjects such as conjugate points and the Morse index, the injectivity radius, the group of isometries and the Myers-Steenrod theorem, and Donaldson's differential geometric approach to Lie algebra theory.