5 edition of Differential geometric structures found in the catalog.
Differential geometric structures
Walter A. Poor
|Statement||Walter A. Poor.|
|LC Classifications||QA641 .P616|
|The Physical Object|
|Pagination||xiii, 338 p. :|
|Number of Pages||338|
|LC Control Number||80019888|
From the point of view of differential topology, the donut and the coffee cup are the same in a sense. In particular, Geometry is a bridge between pure mathematics and natural sciences, first of all physics. The only book I have found that is sort of along these lines is Nicolaescu's Lectures on the Geometry of Manifolds, but this book misses many topics. Main article: Finsler manifold Finsler geometry has Finsler manifolds as the main object of study. But an important distinction is that the geometer does not need the entire object to decide this.
So there is allways a need for new introductory books, and Walschap's book is a good one of these. It obtained a new impulse in the sixties when the complete integrability of the Korteweg-de Vries equation was found and it became clear that some basic and quite general geometrical and algebraic structures govern this property of integrability. Nowadays the geometrical and algebraic approach to partial differential equations constitutes a special branch of modern mathematics. Edit: there are many excellent recommendations I particularly like the Index theory text mentioned by Gordon Craig in the comments as it doesn't shy away from analysis, and does so many things in geometry plus has extensive references below. Readership Graduate students and research mathematicians interested in modern geometry and its applications. I also wanted to focus on differential geometry and not differential topology.
But an important distinction is that the geometer does not need the entire object to decide this. I also wanted to focus on differential geometry and not differential topology. For a really fast exposition of Riemannian geometry, there's a chapter in Milnor's "Morse Theory" that is a classic. They both study primarily the properties of differentiable manifolds, sometimes with a variety of structures imposed on them. The material presented is of interest to those who work in pure and applied mathematics and especially in mathematical physics. The first chapters of the book are suitable for a one-semester course on manifolds.
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From the point of view of differential topology, the donut and the coffee cup are the same in a sense. Geometric theory of Hamiltonian systems, which describe many physical phenomena, led to the development of symplectic and Poisson geometry.
Taimanov The book presents the basics of Riemannian geometry in its modern form as geometry of differentiable manifolds and the most important structures on them. Nowadays the geometrical and algebraic approach to partial differential equations constitutes a special branch of modern mathematics.
Differential topology also deals with questions like these, which specifically pertain to the properties of differentiable mappings on R. Michel Kervaire exhibited topological manifolds with no smooth structure at all. These are the closest analogues to the "ordinary" plane and space considered in Euclidean and non-Euclidean geometry.
Readership Graduate students and research mathematicians interested in modern geometry and its applications. It is a worthwhile addition to any mathematical library. The only book I have found that is sort of along these lines is Nicolaescu's Lectures on the Geometry of Manifolds, but this book misses many topics.
A diffeomorphism between two symplectic manifolds which preserves the symplectic form is called a symplectomorphism. Riemannian manifolds are special cases of the more general Finsler manifolds. Included are the topics usually found in a course on differentiable manifolds, such as vector bundles, tensors, differential forms, de Rham cohomology, the Frobenius theorem and basic Lie group theory.
But the age of those books is showing in terms of what people are really doing today compared to what you learn from using those books.
The presentation is clear, detailed and essentially self-contained. By looking, for instance, at just a tiny piece of the handle, he can decide that the coffee cup is different from the donut because the handle is thinner or more curved than any piece of the donut.
He has a book on Riemannian geometry, but I don't know it very well. In this attractive, inexpensive paperback edition, it belongs in the library of any mathematician or student of mathematics interested in differential geometry.
Description[ edit ] Differential topology considers the properties and structures that require only a smooth structure on a manifold to be defined. Main article: Symplectic geometry Symplectic geometry is the study of symplectic manifolds. Each section ends with exercises.
A selection of more difficult problems has been included to challenge the ambitious student. One other reference that I found which people may find interesting is the following: link and link2 where Prof. The series of definitions, concepts and theories are punctuated by examples, remarks.Lectures on Classical Differential Geometry: Second Edition - Ebook written by Dirk J.
Struik. Read this book using Google Play Books app on your PC, android, iOS devices. Download for offline reading, highlight, bookmark or take notes while you read Lectures 5/5(1).
book by Struik . The more descriptive guide by Hilbert and Cohn-Vossen is also highly recommended. This book covers both geometry and diﬀerential geome-try essentially without the use of calculus. It contains many interesting results and gives excellent descriptions of many of the constructions and results in diﬀerential geometry.
Since the late 19th century, differential geometry has grown into a field concerned more generally with the geometric structures on differentiable manifolds.
Differential geometry is closely related to differential topology and the geometric aspects of the theory of differential equations. Alan Kennington's very extensive list of textbook recommendations in differential geometry offers several suggestions, notably. Serge Lang, Fundamentals of differential geometry Walter Poor, Differential geometric structures, with contents: Chapter 1: An Introduction to fiber bundles (principal and associated bundles, vector bundles and section).
In a more general setting, Vinogradov () has pointed out a simple and natural relationship between the algebra of differential invariants of homogeneous geometric structures and their. Jun 05, · Differential Geometric Structures by Walter A.
Poor,available at Book Depository with free delivery worldwide.5/5(2).