Submanifolds and Holonomy
CRC Press, Apr 28, 2003 - Mathematics - 352 pages
With special emphasis on new techniques based on the holonomy of the normal connection, this book provides a modern, self-contained introduction to submanifold geometry. It offers a thorough survey of these techniques and their applications and presents a framework for various recent results to date found only in scattered research papers. The treatment introduces all the basics of the subject, and along with some classical results and hard-to-find proofs, presents new proofs of several recent results. Appendices furnish the necessary background material, exercises give readers practice in using the techniques, and discussion of open problems stimulates readers' interest in the field.
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Basics of submanifold theory in space forms
21 The fundamental equations for submanifolds of space forms
22 Models of space forms
23 Principal curvatures
24 Totally geodesic submanifolds of space forms
25 Reduction of the codimension
26 Totally umbilical submanifolds of space forms
54 Homogeneous isoparametric submanifolds
55 Isoparametric rank
Rank rigidity of submanifolds and normal holonomy of orbits
61 Submanifolds with curvature normals of constant length and rank of homogeneous submanifolds
62 Normal holonomy of orbits
Homogeneous structures on submanifolds
27 Reducibility of submanifolds
Submanifold geometry of orbits
31 Isometric actions of Lie groups
32 Polar actions and srepresentations
33 Equivariant maps
34 Homogeneous submanifolds of Euclidean space
35 Homogeneous submanifolds of hyperbolic spaces
36 Second fundamental form of orbits
37 Symmetric submanifolds
38 Isoparametric hypersurfaces in space forms
39 Algebraically constant second fundamental form
The Normal Holonomy Theorem
41 Normal holonomy
42 The Normal Holonomy Theorem
43 Proof of the Normal Holonomy Theorem
44 Some geometric applications of the Normal Holonomy Theorem
45 Further remarks
Isoparametric submanifolds and their focal manifolds
51 Submersions and isoparametric maps
52 Isoparametric submanifolds and Coxeter groups
53 Geometric properties of submanifolds with constant principal curvatures
71 Homogeneous structures and homogeneity
72 Examples of homogeneous structures
73 Isoparametric submanifolds of higher rank
Submanifolds of Riemannian manifolds
81 Submanifolds and the fundamental equations
82 Focal points and Jacobi vector fields
83 Totally geodesic submanifolds
84 Totally umbilical submanifolds and extrinsic spheres
85 Symmetric submanifolds
Submanifolds of Symmetric Spaces
92 Totally umbilical submanifolds and extrinsic spheres
93 Symmetric submanifolds
94 Submanifolds with parallel second fundamental form
95 Homogeneous hypersurfaces
A2 Lie groups and Lie algebras
A3 Homogeneous spaces
A4 Symmetric spaces and flag manifolds
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Submanifolds and Holonomy. Jurgen Berndt Sergio Console Carlos Olmos. Read it Online! With special emphasis on new techniques based on the holonomy of the ...
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Submanifolds and Holonomy
Submanifolds and Holonomy. Authors: Jurgen Berndt; Sergio Console; Carlos Olmos. ISBN: 978-0-203-49915-3 (electronic). No. of pages: 336 ...
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Submanifolds and Holonomy Jürgen Berndt, Sergio Console, Carlos Olmos, Science & Technology > ... Jürgen Berndt is the author of Submanifolds and Holonomy. ...
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159, Submanifolds and holonomy / J鰕rgen Berndt, Sergio Console, and Carlos Olmos. -- Chapman & Hall/CRC, c2003. -- (Research notes in mathematics ; 434). ...
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Submanifolds and Holonomy (Submanifolds and Holonomy Libros Ingles Mathematics General Chapman & Hall/CRC) N/A Chapman & Hall/CRC ...
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