Critical Point Theory and Submanifold Geometry
Author: Richard S. Palais
Publisher: Springer
Published: 2006-11-14
Total Pages: 276
ISBN-13: 3540459960
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Geometry And Topology Of Submanifolds, Iii: Proceedings Of The Leeds Differential Geometry Workshop 1990
Author: Alan West
Publisher: World Scientific
Published: 1991-04-22
Total Pages: 336
ISBN-13: 9814611344
DOWNLOAD EBOOKThis workshop collected together works by experts working in various aspects of the differential geometry of submanifold and discussed recent advances and unsolved problems. Two important linking lectures were on the work done by Thorbergsson and others on classifying isoparametric submanifolds of Euclidean spaces and the generalisation of these to Hilbert spaces due to Terng and others. Isoparametric submanifolds provides examples of minimal, taut submanifolds, of harmonic maps and submanifolds with parallel second fundamental form-all topics discussed at this workshop. There were also lectures on the rapidly developing topic of the affine geometry of hypersurfaces and on applications. Amomg the applications discussed are new methods for using PDE's for generating surfaces with special shapes for use in engineering design.
Submanifolds and Holonomy
Author: Jurgen Berndt
Publisher: CRC Press
Published: 2016-02-22
Total Pages: 494
ISBN-13: 1482245167
DOWNLOAD EBOOKSubmanifolds and Holonomy, Second Edition explores recent progress in the submanifold geometry of space forms, including new methods based on the holonomy of the normal connection. This second edition reflects many developments that have occurred since the publication of its popular predecessor.New to the Second EditionNew chapter on normal holonom
Geometry And Topology Of Submanifolds V - Proceedings Of The Conferences On Differential Geometry And Vision & Theory Of Submanifolds
Author: Franki Dillen
Publisher: World Scientific
Published: 1993-09-30
Total Pages: 362
ISBN-13: 9814552488
DOWNLOAD EBOOKDifferential Geometry: Partial Differential Equations on Manifolds
Author: Robert Everist Greene
Publisher: American Mathematical Soc.
Published: 1993
Total Pages: 585
ISBN-13: 082181494X
DOWNLOAD EBOOKThe first of three parts comprising Volume 54, the proceedings of the Summer Research Institute on Differential Geometry, held at the University of California, Los Angeles, July 1990 (ISBN for the set is 0-8218-1493-1). Part 1 begins with a problem list by S.T. Yau, successor to his 1980 list ( Sem
New Developments in Lie Theory and Geometry
Author: Carolyn Gordon
Publisher: American Mathematical Soc.
Published: 2009
Total Pages: 363
ISBN-13: 0821846515
DOWNLOAD EBOOKThis volume is an outgrowth of the Sixth Workshop on Lie Theory and Geometry, held in the province of Cordoba, Argentina in November 2007. The representation theory and structure theory of Lie groups play a pervasive role throughout mathematics and physics. Lie groups are tightly intertwined with geometry and each stimulates developments in the other. The aim of this volume is to bring to a larger audience the mutually beneficial interaction between Lie theorists and geometers that animated the workshop. Two prominent themes of the representation theoretic articles are Gelfand pairs and the representation theory of real reductive Lie groups. Among the more geometric articles are an exposition of major recent developments on noncompact homogeneous Einstein manifolds and aspects of inverse spectral geometry presented in settings accessible to readers new to the area.
Tight and Taut Submanifolds
Author: Nicolaas Hendrik Kuiper
Publisher: Cambridge University Press
Published: 1997-11-13
Total Pages: 372
ISBN-13: 9780521620475
DOWNLOAD EBOOKFirst published in 1997, this book contains six in-depth articles on various aspects of the field of tight and taut submanifolds and concludes with an extensive bibliography of the entire field. The book is dedicated to the memory of Nicolaas H. Kuiper; the first paper is an unfinished but insightful survey of the field of tight immersions and maps written by Kuiper himself. Other papers by leading researchers in the field treat topics such as the smooth and polyhedral portions of the theory of tight immersions, taut, Dupin and isoparametric submanifolds of Euclidean space, taut submanifolds of arbitrary complete Riemannian manifolds, and real hypersurfaces in complex space forms with special curvature properties. Taken together these articles provide a comprehensive survey of the field and point toward several directions for future research.
The Convenient Setting of Global Analysis
Author: Andreas Kriegl
Publisher: American Mathematical Society
Published: 2024-08-15
Total Pages: 631
ISBN-13: 1470478935
DOWNLOAD EBOOKThis book lays the foundations of differential calculus in infinite dimensions and discusses those applications in infinite dimensional differential geometry and global analysis not involving Sobolev completions and fixed point theory. The approach is simple: a mapping is called smooth if it maps smooth curves to smooth curves. Up to Fr‚chet spaces, this notion of smoothness coincides with all known reasonable concepts. In the same spirit, calculus of holomorphic mappings (including Hartogs' theorem and holomorphic uniform boundedness theorems) and calculus of real analytic mappings are developed. Existence of smooth partitions of unity, the foundations of manifold theory in infinite dimensions, the relation between tangent vectors and derivations, and differential forms are discussed thoroughly. Special emphasis is given to the notion of regular infinite dimensional Lie groups. Many applications of this theory are included: manifolds of smooth mappings, groups of diffeomorphisms, geodesics on spaces of Riemannian metrics, direct limit manifolds, perturbation theory of operators, and differentiability questions of infinite dimensional representations.
Topics in Mathematical Analysis and Applications
Author: Themistocles M. Rassias
Publisher: Springer
Published: 2014-10-13
Total Pages: 811
ISBN-13: 3319065548
DOWNLOAD EBOOKThis volume presents significant advances in a number of theories and problems of Mathematical Analysis and its applications in disciplines such as Analytic Inequalities, Operator Theory, Functional Analysis, Approximation Theory, Functional Equations, Differential Equations, Wavelets, Discrete Mathematics and Mechanics. The contributions focus on recent developments and are written by eminent scientists from the international mathematical community. Special emphasis is given to new results that have been obtained in the above mentioned disciplines in which Nonlinear Analysis plays a central role. Some review papers published in this volume will be particularly useful for a broader readership in Mathematical Analysis, as well as for graduate students. An attempt is given to present all subjects in this volume in a unified and self-contained manner, to be particularly useful to the mathematical community.
An Invitation to Morse Theory
Author: Liviu Nicolaescu
Publisher: Springer Science & Business Media
Published: 2011-12-02
Total Pages: 366
ISBN-13: 146141105X
DOWNLOAD EBOOKThis self-contained treatment of Morse theory focuses on applications and is intended for a graduate course on differential or algebraic topology, and will also be of interest to researchers. This is the first textbook to include topics such as Morse-Smale flows, Floer homology, min-max theory, moment maps and equivariant cohomology, and complex Morse theory. The reader is expected to have some familiarity with cohomology theory and differential and integral calculus on smooth manifolds. Some features of the second edition include added applications, such as Morse theory and the curvature of knots, the cohomology of the moduli space of planar polygons, and the Duistermaat-Heckman formula. The second edition also includes a new chapter on Morse-Smale flows and Whitney stratifications, many new exercises, and various corrections from the first edition.
