# Takes a modern approach based on the holomony group of the normal connection of a submanifold # Introduces submanifolds in space forms and discusses the fundamental results # Presents the concept of normal holonomy, the Normal Holonomy Theorem, and the proof and applications of that theorem # Applies the tool of normal holonomy to the study of isoparametric submanifolds and their focal manifolds, orbits of linear Lie group actions and homogeneous submanifolds, and homogeneous structures on submanifolds # Discusses generalizations to submanifolds of Riemannian manifolds, particularly of Riemannian symmetric spaces With special emphasis on new techniques based on the holonomy of the normal connection, this book provides an up-to-date, complete introduction to submanifold geometry. It offers a thorough survey of these techniques and their applications and presents a framework for various recent results to date found only in scattered research papers. The treatment introduces all the basics of the subject, and along with some classical results and hard-to-find proofs, presents new proofs of several recent results. Appendices furnish the necessary background material, exercises give readers practice in using the techniques, and discussion of open problems will help stimulate interest in the field.

Submanifolds and Holonomy

CONSOLE, Sergio;
2003-01-01

Abstract

# Takes a modern approach based on the holomony group of the normal connection of a submanifold # Introduces submanifolds in space forms and discusses the fundamental results # Presents the concept of normal holonomy, the Normal Holonomy Theorem, and the proof and applications of that theorem # Applies the tool of normal holonomy to the study of isoparametric submanifolds and their focal manifolds, orbits of linear Lie group actions and homogeneous submanifolds, and homogeneous structures on submanifolds # Discusses generalizations to submanifolds of Riemannian manifolds, particularly of Riemannian symmetric spaces With special emphasis on new techniques based on the holonomy of the normal connection, this book provides an up-to-date, complete introduction to submanifold geometry. It offers a thorough survey of these techniques and their applications and presents a framework for various recent results to date found only in scattered research papers. The treatment introduces all the basics of the subject, and along with some classical results and hard-to-find proofs, presents new proofs of several recent results. Appendices furnish the necessary background material, exercises give readers practice in using the techniques, and discussion of open problems will help stimulate interest in the field.
2003
CRC Press, Tayloe and Francis group
434
1
336
9781584883715
http://www.crcpress.com/shopping_cart/products/product_detail.asp?sku=C3715&parent_id=&pc=
submanifold geometry; Riemannian geometry; holonomy
J. BERNDT; S. CONSOLE; OLMOS C
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/16163
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