Submanifolds and Holonomy

Berndt J., Olmos C., Console S.1-58053-536-4

Introduces the geometry of submanifolds of space form and the application of new methods based on the holonomy of the normal connection. The monograph explores the central position of s- representations in the framework of submanifold geometry in space forms and presents three tools for their study-reduction of codimensions, Moore’s lemma for local splitting, and the normal holonomy theorem-then applies the tool of normal holonomy to study isoparametric submanifolds and their focal manifolds, orbits of Lie group actions and homogeneous submanifolds, and homogeneous structures on submanifolds. Generalizations to submanifolds of Riemannian manifolds and symmetric spaces close out the book

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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