Submanifolds and holonomy

Jurgen Berndt, Sergio Console, Carlos Olmos1584883715, 9781584883715

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.

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Table of contents :
Cover……Page 1
Preface……Page 10
Contents……Page 14
Ch 1 Introduction……Page 16
Ch 2 Basics of submanifold theory in space forms……Page 22
Ch 3 Submanifold geometry of orbits……Page 48
Ch 4 The Normal Holonomy Theorem……Page 110
Ch 5 Isoparametric submanifolds and their focal manifolds……Page 154
Ch 6 Rank Rigidity of submanifolds and normal holonomy of orbits……Page 192
Ch 7 Homogeneous structures on submanifolds……Page 216
Ch 8 Submanifolds of Riemannian manifolds……Page 238
Ch 9 Submanifolds of Symmetric Space……Page 258
Appendix Basic Material……Page 296
References……Page 328
List of Figures……Page 342
List of Tables……Page 344
Index……Page 346