Submanifolds and holonomy. (2016)

• Record Type: Book
• Further Information: Note: Jürgen Berndt, Sergio Console, Carlos Olmos.
• Authors: Berndt, Jürgen, 1959-; Console, Sergio; Olmos, Carlos
• 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 submanifolds; Isoparametric hypersurfaces in space forms; Algebraically constant second fundamental form The Normal Holonomy Theorem ; Normal holonomy; The normal holonomy theorem; Proof of the normal holonomy theorem; Some geometric applications of the normal holonomy theorem; Further remarks Isoparametric Submanifolds and Their Focal Manifolds ; Submersions and isoparametric maps; Isoparametric submanifolds and Coxeter groups; Geometric properties of submanifolds with constant principal curvatures; Homogeneous isoparametric submanifolds; Isoparametric rank Rank Rigidity of Submanifolds and Normal Holonomy of Orbits ; Submanifolds with curvature normals of constant length and rank of homogeneous submanifolds; Normal holonomy of orbits Homogeneous Structures on Submanifolds ; Homogeneous structures and homogeneity; Examples of homogeneous structures; Isoparametric submanifolds of higher rank Normal 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 submanifolds; Totally umbilical submanifolds and extrinsic spheres; Symmetric submanifolds Submanifolds of Symmetric Spaces ; Totally geodesic submanifolds; Totally umbilical submanifolds and extrinsic spheres; Symmetric 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 Material Exercises appear at the end of each chapter.
• Edition: Second edition
• Publisher Details: Boca Raton : Chapman & Hall/CRC
• Publication Date: 2016
• Extent: 1 online resource, illustrations (black and white)
• Subjects: 516.362; Submanifolds; Holonomy groups
• Languages: English
• ISBNs: 9781482245165
• Related ISBNs: 9781482245158
• Notes: Note: Description based on CIP data; item not viewed.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
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