Lie Sphere Geometry PDF Download
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Author | : Thomas E. Cecil |
Publisher | : Springer Science & Business Media |
Total Pages | : 214 |
Release | : 2007-11-26 |
Genre | : Mathematics |
ISBN | : 0387746552 |
Download Lie Sphere Geometry Book in PDF, ePub and Kindle
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 |
Total Pages | : 219 |
Release | : 2013-03-09 |
Genre | : Mathematics |
ISBN | : 1475740964 |
Download Lie Sphere Geometry Book in PDF, ePub and Kindle
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 | : |
Total Pages | : 224 |
Release | : 2014-01-15 |
Genre | : |
ISBN | : 9781475740974 |
Download Lie Sphere Geometry Book in PDF, ePub and Kindle
Author | : Thomas E. Cecil |
Publisher | : Springer Science & Business Media |
Total Pages | : 214 |
Release | : 2007-10-29 |
Genre | : Mathematics |
ISBN | : 0387746560 |
Download Lie Sphere Geometry Book in PDF, ePub and Kindle
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 | : |
Total Pages | : 101 |
Release | : 2012 |
Genre | : Geometry, Differential |
ISBN | : |
Download Lie Sphere Geometry and Dupin Hypersurfaces Book in PDF, ePub and Kindle
Author | : Boris Odehnal |
Publisher | : Springer |
Total Pages | : 606 |
Release | : 2020-04-29 |
Genre | : Mathematics |
ISBN | : 9783662610527 |
Download The Universe of Quadrics Book in PDF, ePub and Kindle
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 | : George Weston Briggs |
Publisher | : |
Total Pages | : |
Release | : 1905 |
Genre | : |
ISBN | : |
Download Pluecker's Line Geometry and Lie's Sphere Geometry, an Example of Generalized Duality Book in PDF, ePub and Kindle
Author | : Julian Lowell Coolidge |
Publisher | : |
Total Pages | : 603 |
Release | : 1916 |
Genre | : Circle |
ISBN | : |
Download A Treatise on the Circle and the Sphere Book in PDF, ePub and Kindle
Author | : Evgenij V. Feropontov |
Publisher | : |
Total Pages | : 30 |
Release | : 1997 |
Genre | : |
ISBN | : |
Download Surfaces in Lie Sphere Geometry and the Stationary Davey-Stewartson Hierarchy Book in PDF, ePub and Kindle
Author | : D.H. Sattinger |
Publisher | : Springer Science & Business Media |
Total Pages | : 218 |
Release | : 2013-11-11 |
Genre | : Mathematics |
ISBN | : 1475719108 |
Download Lie Groups and Algebras with Applications to Physics, Geometry, and Mechanics Book in PDF, ePub and Kindle
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.