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Submanifolds and Holonomy (Revised) (Hardcover) (Jurgen Berndt & Sergio Console & Carlos Enrique Olmos)
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This book provides an introduction to submanifold geometry with a special emphasis on new techniques based on the holonomy of the normal connection. This second edition includes five new chapters on the normal holonomy of complex submanifolds, the Berger–Simons holonomy theorem, the skew-torsion holonomy theorem, and polar actions on symmetric spaces of compact type and noncompact type. It also adds more than 100 references to the bibliography and substantially improves the index. The book introduces all the basics of the subject, along with some classical results and hard-to-find proofs. It also presents new proofs of several recent results.