Differential Geometry Global Analysis And Topology
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| Author | : Canadian Mathematical Society. Summer Meeting |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 198 |
| Release | : 1992 |
| Genre | : Mathematics |
| ISBN | : 9780821860175 |
This book contains the proceedings of a special session held during the Summer Meeting of the Canadian Mathematical Society in 1990. The articles collected here reflect the diverse interests of the participants but are united by the common theme of the interplay among geometry, global analysis, and topology. The topics covered include applications to low dimensional manifolds, control theory, integrable systems, Lie algebras of operators, and algebraic geometry and provide an insight into some recent trends in these areas.
| Author | : Ilka Agricola |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 362 |
| Release | : 2002 |
| Genre | : Mathematics |
| ISBN | : 0821829513 |
The final third of the book applies the mathematical ideas to important areas of physics: Hamiltonian mechanics, statistical mechanics, and electrodynamics." "There are many classroom-tested exercises and examples with excellent figures throughout. The book is ideal as a text for a first course in differential geometry, suitable for advanced undergraduates or graduate students in mathematics or physics."--BOOK JACKET.
| 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 | : Werner Ballmann |
| Publisher | : Birkhäuser |
| Total Pages | : 174 |
| Release | : 2018-07-18 |
| Genre | : Mathematics |
| ISBN | : 3034809832 |
This book provides an introduction to topology, differential topology, and differential geometry. It is based on manuscripts refined through use in a variety of lecture courses. The first chapter covers elementary results and concepts from point-set topology. An exception is the Jordan Curve Theorem, which is proved for polygonal paths and is intended to give students a first glimpse into the nature of deeper topological problems. The second chapter of the book introduces manifolds and Lie groups, and examines a wide assortment of examples. Further discussion explores tangent bundles, vector bundles, differentials, vector fields, and Lie brackets of vector fields. This discussion is deepened and expanded in the third chapter, which introduces the de Rham cohomology and the oriented integral and gives proofs of the Brouwer Fixed-Point Theorem, the Jordan-Brouwer Separation Theorem, and Stokes's integral formula. The fourth and final chapter is devoted to the fundamentals of differential geometry and traces the development of ideas from curves to submanifolds of Euclidean spaces. Along the way, the book discusses connections and curvature--the central concepts of differential geometry. The discussion culminates with the Gauß equations and the version of Gauß's theorema egregium for submanifolds of arbitrary dimension and codimension. This book is primarily aimed at advanced undergraduates in mathematics and physics and is intended as the template for a one- or two-semester bachelor's course.
| Author | : Dirk Ferus |
| Publisher | : Springer |
| Total Pages | : 289 |
| Release | : 2006-11-14 |
| Genre | : Mathematics |
| ISBN | : 354046445X |
All papers appearing in this volume are original research articles and have not been published elsewhere. They meet the requirements that are necessary for publication in a good quality primary journal. E.Belchev, S.Hineva: On the minimal hypersurfaces of a locally symmetric manifold. -N.Blasic, N.Bokan, P.Gilkey: The spectral geometry of the Laplacian and the conformal Laplacian for manifolds with boundary. -J.Bolton, W.M.Oxbury, L.Vrancken, L.M. Woodward: Minimal immersions of RP2 into CPn. -W.Cieslak, A. Miernowski, W.Mozgawa: Isoptics of a strictly convex curve. -F.Dillen, L.Vrancken: Generalized Cayley surfaces. -A.Ferrandez, O.J.Garay, P.Lucas: On a certain class of conformally flat Euclidean hypersurfaces. -P.Gauduchon: Self-dual manifolds with non-negative Ricci operator. -B.Hajduk: On the obstruction group toexistence of Riemannian metrics of positive scalar curvature. -U.Hammenstaedt: Compact manifolds with 1/4-pinched negative curvature. -J.Jost, Xiaowei Peng: The geometry of moduli spaces of stable vector bundles over Riemannian surfaces. - O.Kowalski, F.Tricerri: A canonical connection for locally homogeneous Riemannian manifolds. -M.Kozlowski: Some improper affine spheres in A3. -R.Kusner: A maximum principle at infinity and the topology of complete embedded surfaces with constant mean curvature. -Anmin Li: Affine completeness and Euclidean completeness. -U.Lumiste: On submanifolds with parallel higher order fundamental form in Euclidean spaces. -A.Martinez, F.Milan: Convex affine surfaces with constant affine mean curvature. -M.Min-Oo, E.A.Ruh, P.Tondeur: Transversal curvature and tautness for Riemannian foliations. -S.Montiel, A.Ros: Schroedinger operators associated to a holomorphic map. -D.Motreanu: Generic existence of Morse functions on infinite dimensional Riemannian manifolds and applications. -B.Opozda: Some extensions of Radon's theorem.
| Author | : Xianzhe Dai |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 401 |
| Release | : 2012-06-01 |
| Genre | : Mathematics |
| ISBN | : 3034802579 |
Metric and Differential Geometry grew out of a similarly named conference held at Chern Institute of Mathematics, Tianjin and Capital Normal University, Beijing. The various contributions to this volume cover a broad range of topics in metric and differential geometry, including metric spaces, Ricci flow, Einstein manifolds, Kähler geometry, index theory, hypoelliptic Laplacian and analytic torsion. It offers the most recent advances as well as surveys the new developments. Contributors: M.T. Anderson J.-M. Bismut X. Chen X. Dai R. Harvey P. Koskela B. Lawson X. Ma R. Melrose W. Müller A. Naor J. Simons C. Sormani D. Sullivan S. Sun G. Tian K. Wildrick W. Zhang
| Author | : Fangyang Zheng |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 275 |
| Release | : 2000 |
| Genre | : Mathematics |
| ISBN | : 0821829602 |
Discusses the differential geometric aspects of complex manifolds. This work contains standard materials from general topology, differentiable manifolds, and basic Riemannian geometry. It discusses complex manifolds and analytic varieties, sheaves and holomorphic vector bundles. It also gives a brief account of the surface classification theory.
| Author | : Lawrence Conlon |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 402 |
| Release | : 2013-04-17 |
| Genre | : Mathematics |
| ISBN | : 1475722842 |
This book is based on the full year Ph.D. qualifying course on differentiable manifolds, global calculus, differential geometry, and related topics, given by the author at Washington University several times over a twenty year period. It is addressed primarily to second year graduate students and well prepared first year students. Presupposed is a good grounding in general topology and modern algebra, especially linear algebra and the analogous theory of modules over a commutative, unitary ring. Although billed as a "first course" , the book is not intended to be an overly sketchy introduction. Mastery of this material should prepare the student for advanced topics courses and seminars in differen tial topology and geometry. There are certain basic themes of which the reader should be aware. The first concerns the role of differentiation as a process of linear approximation of non linear problems. The well understood methods of linear algebra are then applied to the resulting linear problem and, where possible, the results are reinterpreted in terms of the original nonlinear problem. The process of solving differential equations (i. e., integration) is the reverse of differentiation. It reassembles an infinite array of linear approximations, result ing from differentiation, into the original nonlinear data. This is the principal tool for the reinterpretation of the linear algebra results referred to above.
| Author | : Ana Hurtado |
| Publisher | : Springer Nature |
| Total Pages | : 121 |
| Release | : 2020-08-19 |
| Genre | : Mathematics |
| ISBN | : 3030552934 |
This book contains a clear exposition of two contemporary topics in modern differential geometry: distance geometric analysis on manifolds, in particular, comparison theory for distance functions in spaces which have well defined bounds on their curvature the application of the Lichnerowicz formula for Dirac operators to the study of Gromov's invariants to measure the K-theoretic size of a Riemannian manifold. It is intended for both graduate students and researchers.
| Author | : Dirk Ferus |
| Publisher | : Springer |
| Total Pages | : 344 |
| Release | : 2006-11-14 |
| Genre | : Mathematics |
| ISBN | : 3540396985 |
