Download E-books Modern Geometry Methods and Applications: Part II: The Geometry and Topology of Manifolds (Graduate Texts in Mathematics) (Part 2) PDF

By B.A. Dubrovin

Up till lately, Riemannian geometry and easy topology weren't incorporated, even by means of departments or colleges of arithmetic, as obligatory topics in a university-level mathematical schooling. the normal classes within the classical differential geometry of curves and surfaces which have been given in its place (and nonetheless are given in a few areas) have come progressively to be seen as anachronisms. notwithstanding, there was hitherto no unanimous contract as to precisely how such classes will be cited so far, that's to assert, which elements of recent geometry may be considered as totally necessary to a latest mathematical schooling, and what will be definitely the right point of abstractness in their exposition. the duty of designing a modernized path in geometry used to be began in 1971 within the mechanics department of the school of Mechanics and arithmetic of Moscow nation college. The subject-matter and point of abstractness of its exposition have been dictated by means of the view that, as well as the geometry of curves and surfaces, the next subject matters are definitely necessary within the a number of parts of software of arithmetic (especially in elasticity and relativity, to call yet two), and are for this reason crucial: the speculation of tensors (including covariant differentiation of them); Riemannian curvature; geodesics and the calculus of diversifications (including the conservation legislation and Hamiltonian formalism); the actual case of skew-symmetric tensors (i. e.

Show description

Read or Download Modern Geometry Methods and Applications: Part II: The Geometry and Topology of Manifolds (Graduate Texts in Mathematics) (Part 2) PDF

Similar Differential Geometry books

Surgery on Simply-Connected Manifolds

This publication is an exposition of the means of surgical procedure on simply-connected delicate manifolds. Systematic research of differentiable manifolds utilizing those rules was once began through Milnor [45] and Wallace [68] and constructed generally within the final ten years. it truly is now attainable to offer a fairly whole idea of simply-connected manifolds of size ~ five utilizing this strategy and that's what i'm going to try and start the following.

Lie Sphere Geometry: With Applications to Submanifolds (Universitext)

Thomas Cecil is a math professor with an unrivalled take hold of of Lie Sphere Geometry. right here, he offers a transparent and finished smooth therapy of the topic, in addition to its functions to the examine of Euclidean submanifolds. It starts off with the development of the distance of spheres, together with the basic notions of orientated touch, parabolic pencils of spheres, and Lie sphere alterations.

The Geometry of Kerr Black Holes (Dover Books on Physics)

This designated monograph by way of a famous UCLA professor examines intimately the maths of Kerr black holes, which own the houses of mass and angular momentum yet hold no electric cost. compatible for complicated undergraduates and graduate scholars of arithmetic, physics, and astronomy in addition to specialist physicists, the self-contained remedy constitutes an creation to fashionable thoughts in differential geometry.

The Penrose Transform: Its Interaction with Representation Theory (Dover Books on Mathematics)

"Brings to the reader a massive volume of data, good prepared and condensed into under 2 hundred pages. " — Mathematical ReviewsIn fresh a long time twistor idea has turn into an immense concentration for college kids of mathematical physics. primary to twistor idea is the geometrical rework often called the Penrose rework, named for its groundbreaking developer.

Extra info for Modern Geometry Methods and Applications: Part II: The Geometry and Topology of Manifolds (Graduate Texts in Mathematics) (Part 2)

Show sample text content

V. Pogorelov, Ju. F. Borisov, V. A. Toponogov and V. I. Kuz'minov, who during reviewing the e-book contributed many helpful reviews. We additionally thank Ja. B. Zel'dovie for numerous observations resulting in advancements within the exposition at numerous issues, in connexion with the instruction of the English and French versions of this e-book. We provide our certain thank you additionally to the students who facilitated the duty of incorporating the fewer general fabric into the e-book. for example the evidence of Liouville's theorem on conformal alterations, which isn't to be present in the traditional literature, used to be communicated to us via V. A. Zorie. The editor D. B. Fuks simplified the proofs of a number of theorems. we're thankful additionally to O. T. Bogojavlenskii, M. I. Monastyrskii, S. G. Gindikin, D. V. Alekseevskii, I. V. Gribkov, P. G. Grinevie, and E. B. Vinberg. x Preface Translator's acknowledgments. thank you are as a result of Abe Shenitzer for far type suggestion and encouragement, to numerous others of my colleagues for placing their services at my disposal, and to Eadie Henry for her first-class typing and nice persistence. Contents bankruptcy 1 Examples of Manifolds §1. the concept that of a manifold 1. 1. Definition of a manifold 1. 2. Mappings of manifolds; tensors on manifolds 1. three. Embeddings and immersions of manifolds. Manifolds with boundary §2. the best examples of manifolds 2. 1. Surfaces in Euclidean house. Transformation teams as manifolds 2. 2. Projective areas 2. three. workouts §3. crucial evidence from the idea of Lie teams three. 1. The constitution of a neighbourhood of the id of a Lie workforce. The Lie algebra of a Lie crew. Semisimplicity three. 2. the idea that of a linear illustration. An instance of a non-matrix Lie crew §4. advanced manifolds four. 1. Definitions and examples four. 2. Riemann surfaces as manifolds §5. the easiest homogeneous areas five. 1. motion of a gaggle on a manifold . five. 2. Examples of homogeneous areas five. three. workouts §6. areas of continuous curvature (symmetric areas) 6. 1. the concept that of a symmetric house 6. 2. The isometry workforce of a manifold. homes of its Lie algebra 6. three. Symmetric areas of the 1st and moment varieties 6. four. Lie teams as symmetric areas 6. five. developing symmetric areas. Examples 6. 6. workouts 1 1 I five nine 10 10 15 19 20 20 28 31 31 37 forty-one forty-one forty two forty six forty six forty six forty nine fifty one fifty three S5 S8 XII §7. Vector bundles on a manifold 7. 1. buildings related to tangent vectors 7. 2. the traditional vector package deal on a submanifold Contents fifty nine fifty nine sixty two bankruptcy 2 Foundational Questions. crucial proof relating capabilities on a Manifold. commonplace soft Mappings §8. walls of harmony and their purposes eight. 1. walls of cohesion eight. 2. the best purposes of walls of solidarity. Integrals over a manifold and the overall Stokes formulation eight. three. Invariant metrics §9. the conclusion of compact manifolds as surfaces in lR/Y §1O. numerous homes of delicate maps of manifolds 10. 1. Approximation of constant mappings by way of delicate ones 10. 2. Sard's theorem 10. three. Transversal regularity 10. four. Morse capabilities §11. purposes of Sard's theorem eleven. 1. The life of embeddings and immersions eleven.

Rated 4.11 of 5 – based on 16 votes