Natural Operations In Differential Geometry PDF Download
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| Author | : Ivan Kolar |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 440 |
| Release | : 2013-03-09 |
| Genre | : Mathematics |
| ISBN | : 3662029502 |
Download Natural Operations in Differential Geometry Book in PDF, ePub and Kindle
The aim of this work is threefold: First it should be a monographical work on natural bundles and natural op erators in differential geometry. This is a field which every differential geometer has met several times, but which is not treated in detail in one place. Let us explain a little, what we mean by naturality. Exterior derivative commutes with the pullback of differential forms. In the background of this statement are the following general concepts. The vector bundle A kT* M is in fact the value of a functor, which associates a bundle over M to each manifold M and a vector bundle homomorphism over f to each local diffeomorphism f between manifolds of the same dimension. This is a simple example of the concept of a natural bundle. The fact that exterior derivative d transforms sections of A kT* M into sections of A k+1T* M for every manifold M can be expressed by saying that d is an operator from A kT* M into A k+1T* M.
| Author | : Joel W. Robbin |
| Publisher | : Springer Nature |
| Total Pages | : 426 |
| Release | : 2022-01-12 |
| Genre | : Mathematics |
| ISBN | : 3662643405 |
Download Introduction to Differential Geometry Book in PDF, ePub and Kindle
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.
| Author | : Toshiaki Adachi |
| Publisher | : World Scientific |
| Total Pages | : 257 |
| Release | : 2022-04-07 |
| Genre | : Mathematics |
| ISBN | : 9811248117 |
Download New Horizons In Differential Geometry And Its Related Fields Book in PDF, ePub and Kindle
This volume presents recent developments in geometric structures on Riemannian manifolds and their discretizations. With chapters written by recognized experts, these discussions focus on contact structures, Kähler structures, fiber bundle structures and Einstein metrics. It also contains works on the geometric approach on coding theory.For researchers and students, this volume forms an invaluable source to learn about these subjects that are not only in the field of differential geometry but also in other wide related areas. It promotes and deepens the study of geometric structures.
| Author | : Erwin Kreyszig |
| Publisher | : Courier Corporation |
| Total Pages | : 384 |
| Release | : 2013-04-26 |
| Genre | : Mathematics |
| ISBN | : 0486318621 |
Download Differential Geometry Book in PDF, ePub and Kindle
An introductory textbook on the differential geometry of curves and surfaces in 3-dimensional Euclidean space, presented in its simplest, most essential form. With problems and solutions. Includes 99 illustrations.
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| Total Pages | : |
| Release | : 2000 |
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Download Elementary Differential Geometry Book in PDF, ePub and Kindle
| Author | : Torsten Wedhorn |
| Publisher | : Springer |
| Total Pages | : 366 |
| Release | : 2016-07-25 |
| Genre | : Mathematics |
| ISBN | : 3658106336 |
Download Manifolds, Sheaves, and Cohomology Book in PDF, ePub and Kindle
This book explains techniques that are essential in almost all branches of modern geometry such as algebraic geometry, complex geometry, or non-archimedian geometry. It uses the most accessible case, real and complex manifolds, as a model. The author especially emphasizes the difference between local and global questions. Cohomology theory of sheaves is introduced and its usage is illustrated by many examples.
| Author | : Andrew McInerney |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 420 |
| Release | : 2013-07-09 |
| Genre | : Mathematics |
| ISBN | : 1461477328 |
Download First Steps in Differential Geometry Book in PDF, ePub and Kindle
Differential geometry arguably offers the smoothest transition from the standard university mathematics sequence of the first four semesters in calculus, linear algebra, and differential equations to the higher levels of abstraction and proof encountered at the upper division by mathematics majors. Today it is possible to describe differential geometry as "the study of structures on the tangent space," and this text develops this point of view. This book, unlike other introductory texts in differential geometry, develops the architecture necessary to introduce symplectic and contact geometry alongside its Riemannian cousin. The main goal of this book is to bring the undergraduate student who already has a solid foundation in the standard mathematics curriculum into contact with the beauty of higher mathematics. In particular, the presentation here emphasizes the consequences of a definition and the careful use of examples and constructions in order to explore those consequences.
| Author | : Heinrich W. Guggenheimer |
| Publisher | : Courier Corporation |
| Total Pages | : 404 |
| Release | : 2012-04-27 |
| Genre | : Mathematics |
| ISBN | : 0486157202 |
Download Differential Geometry Book in PDF, ePub and Kindle
This text contains an elementary introduction to continuous groups and differential invariants; an extensive treatment of groups of motions in euclidean, affine, and riemannian geometry; more. Includes exercises and 62 figures.
| Author | : Gerald Jay Sussman |
| Publisher | : MIT Press |
| Total Pages | : 249 |
| Release | : 2013-07-05 |
| Genre | : Mathematics |
| ISBN | : 0262019345 |
Download Functional Differential Geometry Book in PDF, ePub and Kindle
An explanation of the mathematics needed as a foundation for a deep understanding of general relativity or quantum field theory. Physics is naturally expressed in mathematical language. Students new to the subject must simultaneously learn an idiomatic mathematical language and the content that is expressed in that language. It is as if they were asked to read Les Misérables while struggling with French grammar. This book offers an innovative way to learn the differential geometry needed as a foundation for a deep understanding of general relativity or quantum field theory as taught at the college level. The approach taken by the authors (and used in their classes at MIT for many years) differs from the conventional one in several ways, including an emphasis on the development of the covariant derivative and an avoidance of the use of traditional index notation for tensors in favor of a semantically richer language of vector fields and differential forms. But the biggest single difference is the authors' integration of computer programming into their explanations. By programming a computer to interpret a formula, the student soon learns whether or not a formula is correct. Students are led to improve their program, and as a result improve their understanding.
| Author | : Leonor Godinho |
| Publisher | : Springer |
| Total Pages | : 476 |
| Release | : 2014-07-26 |
| Genre | : Mathematics |
| ISBN | : 3319086669 |
Download An Introduction to Riemannian Geometry Book in PDF, ePub and Kindle
Unlike many other texts on differential geometry, this textbook also offers interesting applications to geometric mechanics and general relativity. The first part is a concise and self-contained introduction to the basics of manifolds, differential forms, metrics and curvature. The second part studies applications to mechanics and relativity including the proofs of the Hawking and Penrose singularity theorems. It can be independently used for one-semester courses in either of these subjects. The main ideas are illustrated and further developed by numerous examples and over 300 exercises. Detailed solutions are provided for many of these exercises, making An Introduction to Riemannian Geometry ideal for self-study.
