Submanifolds and Holonomy, Second Edition (Monographs and Research Notes in Mathematics) by Jurgen Berndt, Sergio Console, Carlos Enrique Olmos
2016 | ISBN: 1482245159 | English | 494 pages | PDF | 8 MB
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, Moores 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.