Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Lie Sphere Geometry PDF full book. Access full book title Lie Sphere Geometry by Thomas E. Cecil. Download full books in PDF and EPUB format.
Author: Thomas E. Cecil Publisher: Springer Science & Business Media ISBN: 0387746552 Category : Mathematics Languages : en Pages : 214
Book Description
Thomas Cecil is a math professor with an unrivalled grasp of Lie Sphere Geometry. Here, he provides a clear and comprehensive modern treatment of the subject, as well as its applications to the study of Euclidean submanifolds. It begins with the construction of the space of spheres, including the fundamental notions of oriented contact, parabolic pencils of spheres, and Lie sphere transformations. This new edition contains revised sections on taut submanifolds, compact proper Dupin submanifolds, reducible Dupin submanifolds, and the cyclides of Dupin. Completely new material on isoparametric hypersurfaces in spheres and Dupin hypersurfaces with three and four principal curvatures is also included. The author surveys the known results in these fields and indicates directions for further research and wider application of the methods of Lie sphere geometry.
Author: Thomas E. Cecil Publisher: Springer Science & Business Media ISBN: 1475740964 Category : Mathematics Languages : en Pages : 219
Book Description
Lie Sphere Geometry provides a modern treatment of Lie's geometry of spheres, its recent applications and the study of Euclidean space. This book begins with Lie's construction of the space of spheres, including the fundamental notions of oriented contact, parabolic pencils of spheres and Lie sphere transformation. The link with Euclidean submanifold theory is established via the Legendre map. This provides a powerful framework for the study of submanifolds, especially those characterized by restrictions on their curvature spheres. Of particular interest are isoparametric, Dupin and taut submanifolds. These have recently been classified up to Lie sphere transformation in certain special cases through the introduction of natural Lie invariants. The author provides complete proofs of these classifications and indicates directions for further research and wider application of these methods.
Author: Thomas E. Cecil Publisher: Springer Science & Business Media ISBN: 0387746552 Category : Mathematics Languages : en Pages : 214
Book Description
Thomas Cecil is a math professor with an unrivalled grasp of Lie Sphere Geometry. Here, he provides a clear and comprehensive modern treatment of the subject, as well as its applications to the study of Euclidean submanifolds. It begins with the construction of the space of spheres, including the fundamental notions of oriented contact, parabolic pencils of spheres, and Lie sphere transformations. This new edition contains revised sections on taut submanifolds, compact proper Dupin submanifolds, reducible Dupin submanifolds, and the cyclides of Dupin. Completely new material on isoparametric hypersurfaces in spheres and Dupin hypersurfaces with three and four principal curvatures is also included. The author surveys the known results in these fields and indicates directions for further research and wider application of the methods of Lie sphere geometry.
Author: Thomas E. Cecil Publisher: Springer Science & Business Media ISBN: 0387746560 Category : Mathematics Languages : en Pages : 214
Book Description
Thomas Cecil is a math professor with an unrivalled grasp of Lie Sphere Geometry. Here, he provides a clear and comprehensive modern treatment of the subject, as well as its applications to the study of Euclidean submanifolds. It begins with the construction of the space of spheres, including the fundamental notions of oriented contact, parabolic pencils of spheres, and Lie sphere transformations. This new edition contains revised sections on taut submanifolds, compact proper Dupin submanifolds, reducible Dupin submanifolds, and the cyclides of Dupin. Completely new material on isoparametric hypersurfaces in spheres and Dupin hypersurfaces with three and four principal curvatures is also included. The author surveys the known results in these fields and indicates directions for further research and wider application of the methods of Lie sphere geometry.
Author: Boris Odehnal Publisher: Springer ISBN: 9783662610558 Category : Mathematics Languages : en Pages : 606
Book Description
The Universe of Quadrics This text presents the theory of quadrics in a modern form. It builds on the previously published book "The Universe of Conics", including many novel results that are not easily accessible elsewhere. As in the conics book, the approach combines synthetic and analytic methods to derive projective, affine, and metrical properties, covering both Euclidean and non-Euclidean geometries. While the history of conics is more than two thousand years old, the theory of quadrics began to develop approximately three hundred years ago. Quadrics play a fundamental role in numerous fields of mathematics and physics, their applications ranging from mechanical engineering, architecture, astronomy, and design to computer graphics. This text will be invaluable to undergraduate and graduate mathematics students, those in adjacent fields of study, and anyone with a deeper interest in geometry. Complemented with about three hundred fifty figures and photographs, this innovative text will enhance your understanding of projective geometry, linear algebra, mechanics, and differential geometry, with careful exposition and many illustrative exercises.
Author: Simon Brendle Publisher: American Mathematical Soc. ISBN: 0821849387 Category : Ricci flow Languages : en Pages : 186
Book Description
Deals with the Ricci flow, and the convergence theory for the Ricci flow. This title focuses on preserved curvature conditions, such as positive isotropic curvature. It is suitable for graduate students and researchers.
Author: D.H. Sattinger Publisher: Springer Science & Business Media ISBN: 1475719108 Category : Mathematics Languages : en Pages : 218
Book Description
This book is intended as an introductory text on the subject of Lie groups and algebras and their role in various fields of mathematics and physics. It is written by and for researchers who are primarily analysts or physicists, not algebraists or geometers. Not that we have eschewed the algebraic and geo metric developments. But we wanted to present them in a concrete way and to show how the subject interacted with physics, geometry, and mechanics. These interactions are, of course, manifold; we have discussed many of them here-in particular, Riemannian geometry, elementary particle physics, sym metries of differential equations, completely integrable Hamiltonian systems, and spontaneous symmetry breaking. Much ofthe material we have treated is standard and widely available; but we have tried to steer a course between the descriptive approach such as found in Gilmore and Wybourne, and the abstract mathematical approach of Helgason or Jacobson. Gilmore and Wybourne address themselves to the physics community whereas Helgason and Jacobson address themselves to the mathematical community. This book is an attempt to synthesize the two points of view and address both audiences simultaneously. We wanted to present the subject in a way which is at once intuitive, geometric, applications oriented, mathematically rigorous, and accessible to students and researchers without an extensive background in physics, algebra, or geometry.
Author: Thomas E. Cecil Publisher: Springer ISBN: 1493932462 Category : Mathematics Languages : en Pages : 596
Book Description
This exposition provides the state-of-the art on the differential geometry of hypersurfaces in real, complex, and quaternionic space forms. Special emphasis is placed on isoparametric and Dupin hypersurfaces in real space forms as well as Hopf hypersurfaces in complex space forms. The book is accessible to a reader who has completed a one-year graduate course in differential geometry. The text, including open problems and an extensive list of references, is an excellent resource for researchers in this area. Geometry of Hypersurfaces begins with the basic theory of submanifolds in real space forms. Topics include shape operators, principal curvatures and foliations, tubes and parallel hypersurfaces, curvature spheres and focal submanifolds. The focus then turns to the theory of isoparametric hypersurfaces in spheres. Important examples and classification results are given, including the construction of isoparametric hypersurfaces based on representations of Clifford algebras. An in-depth treatment of Dupin hypersurfaces follows with results that are proved in the context of Lie sphere geometry as well as those that are obtained using standard methods of submanifold theory. Next comes a thorough treatment of the theory of real hypersurfaces in complex space forms. A central focus is a complete proof of the classification of Hopf hypersurfaces with constant principal curvatures due to Kimura and Berndt. The book concludes with the basic theory of real hypersurfaces in quaternionic space forms, including statements of the major classification results and directions for further research.
Author: Thomas E. Cecil
Author: Thomas E. Cecil
Author: Thomas E. Cecil
Author: Thomas E. Cecil
Author: Thomas E. Cecil
Author: George Weston Briggs
Author: Boris Odehnal
Author: Julian Lowell Coolidge
Author: Simon Brendle
Author: D.H. Sattinger
Author: Thomas E. Cecil