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Submanifolds and holonomy

Author: Jürgen Berndt; Sergio Console; Carlos Enrique Olmos
Publisher: Boca Raton : CRC Press, [2016] ©2016
Series: Monographs and research notes in mathematics, 21.
Edition/Format:   eBook : Document : English : Second editionView all editions and formats

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Genre/Form: Electronic books
Additional Physical Format: Erscheint auch als:
Berndt, Jurgen. Submanifolds and Holonomy, Second Edition
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Jürgen Berndt; Sergio Console; Carlos Enrique Olmos
ISBN: 9781482245165 1482245167
OCLC Number: 938557169
Notes: "A Chapman & Hall book."
Description: 1 online resource (xxxviii, 443 pages) : illustrations.
Contents: Basics of Submanifold Theory in Space Forms The fundamental equations for submanifolds of space forms Models of space forms Principal curvatures Totally geodesic submanifolds of space forms Reduction of the codimension Totally umbilical submanifolds of space forms Reducibility of submanifolds Submanifold Geometry of Orbits Isometric actions of Lie groups Existence of slices and principal orbits for isometric actions Polar actions and s-representations Equivariant maps Homogeneous submanifolds of Euclidean spaces Homogeneous submanifolds of hyperbolic spaces Second fundamental form of orbits Symmetric submanifoldsIsoparametric hypersurfaces in space forms Algebraically constant second fundamental form The Normal Holonomy Theorem Normal holonomy The normal holonomy theorem Proof of the normal holonomy theoremSome geometric applications of the normal holonomy theoremFurther remarksIsoparametric Submanifolds and Their Focal Manifolds Submersions and isoparametric maps Isoparametric submanifolds and Coxeter groups Geometric properties of submanifolds with constant principal curvatures Homogeneous isoparametric submanifoldsIsoparametric rank Rank Rigidity of Submanifolds and Normal Holonomy of Orbits Submanifolds with curvature normals of constant length and rank of homogeneous submanifoldsNormal holonomy of orbits Homogeneous Structures on Submanifolds Homogeneous structures and homogeneity Examples of homogeneous structures Isoparametric submanifolds of higher rankNormal Holonomy of Complex Submanifolds Polar-like properties of the foliation by holonomy tubes Shape operators with some constant eigenvalues in parallel manifolds The canonical foliation of a full holonomy tube Applications to complex submanifolds of Cn with nontransitive normal holonomy Applications to complex submanifolds of CPn with nontransitive normal holonomy The Berger-Simons Holonomy Theorem Holonomy systems The Simons holonomy theorem The Berger holonomy theorem The Skew-Torsion Holonomy Theorem Fixed point sets of isometries and homogeneous submanifolds Naturally reductive spaces Totally skew one-forms with values in a Lie algebra The derived 2-form with values in a Lie algebra The skew-torsion holonomy theorem Applications to naturally reductive spaces Submanifolds of Riemannian Manifolds Submanifolds and the fundamental equations Focal points and Jacobi fields Totally geodesic submanifoldsTotally umbilical submanifolds and extrinsic spheres Symmetric submanifolds Submanifolds of Symmetric Spaces Totally geodesic submanifolds Totally umbilical submanifolds and extrinsic spheresSymmetric submanifolds Submanifolds with parallel second fundamental form Polar Actions on Symmetric Spaces of Compact Type Polar actions - rank one Polar actions - higher rank Hyperpolar actions - higher rank Cohomogeneity one actions - higher rank Hypersurfaces with constant principal curvatures Polar Actions on Symmetric Spaces of Noncompact Type Dynkin diagrams of symmetric spaces of noncompact type Parabolic subalgebras Polar actions without singular orbits Hyperpolar actions without singular orbits Polar actions on hyperbolic spaces Cohomogeneity one actions - higher rank Hypersurfaces with constant principal curvatures Appendix: Basic MaterialExercises appear at the end of each chapter.
Series Title: Monographs and research notes in mathematics, 21.
Responsibility: Jürgen Berndt, Sergio Console, Carlos Enrique Olmos.


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Praise for the First Edition:"This book is carefully written; it contains some new proofs and open problems, many exercises and references, and an appendix for basic materials, and so it would be Read more...

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