Submanifolds and Holonomy

2nd Edition

Jurgen Berndt, Sergio Console, Carlos Enrique Olmos

Chapman and Hall/CRC
Published February 8, 2016
Reference - 456 Pages - 8 B/W Illustrations
ISBN 9781482245158 - CAT# K23523
Series: Chapman & Hall/CRC Monographs and Research Notes in Mathematics

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Summary

Submanifolds and Holonomy, Second Edition explores recent progress in the submanifold geometry of space forms, including new methods based on the holonomy of the normal connection. This second edition reflects many developments that have occurred since the publication of its popular predecessor.

New to the Second Edition

  • New chapter on normal holonomy of complex submanifolds
  • New chapter on the Berger–Simons holonomy theorem
  • New chapter on the skew-torsion holonomy system
  • New chapter on polar actions on symmetric spaces of compact type
  • New chapter on polar actions on symmetric spaces of noncompact type
  • New section on the existence of slices and principal orbits for isometric actions
  • New subsection on maximal totally geodesic submanifolds
  • New subsection on the index of symmetric spaces

The book uses the reduction of codimension, Moore’s lemma for local splitting, and the normal holonomy theorem to address the geometry of submanifolds. It presents a unified treatment of new proofs and main results of homogeneous submanifolds, isoparametric submanifolds, and their generalizations to Riemannian manifolds, particularly Riemannian symmetric spaces.