Lie Sphere Geometry: With Applications to Submanifolds - Tapa blanda

Libro 80 de 260: Universitext

Cecil, T.E.

 
9783540977476: Lie Sphere Geometry: With Applications to Submanifolds
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ISBN 10: 3540977473 ISBN 13: 9783540977476
Editorial: Springer-Verlag Berlin and Heidelberg GmbH & Co. K, 1992

Sinopsis

This is a modern treatment of Lie's geometry of spheres, its recent applications and the study of Euclidean space. The 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.

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Reseña del editor

This is a modern treatment of Lie's geometry of spheres, its recent applications and the study of Euclidean space. The 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.

"Sobre este título" puede pertenecer a otra edición de este libro.

Editorial
Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Año de publicación
1992
Idioma
Inglés
ISBN 10 
3540977473
ISBN 13 
9783540977476
Encuadernación
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Número de páginas
219
Contacto del fabricante
no disponible
Persona responsable
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Alemania

Otras ediciones populares con el mismo título

9780387746555: Lie Sphere Geometry: With Applications to Submanifolds (Universitext)

Edición Destacada

ISBN 10:  0387746552 ISBN 13:  9780387746555
Editorial: Springer New York, 2010
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