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catalog contributor b12845381.
catalog contributor b12845382.
catalog contributor b12845383.
catalog created "c2003.".
catalog date "2003".
catalog date "c2003.".
catalog dateCopyrighted "c2003.".
catalog description "2 Basics of submanifold theory in space forms 7 -- 2.1 The fundamental equations for submanifolds of space forms 8 -- 2.2 Models of space forms 14 -- 2.3 Principal curvatures 17 -- 2.4 Totally geodesic submanifolds of space forms 20 -- 2.5 Reduction of the codimension 22 -- 2.6 Totally umbilical submanifolds of space forms 24 -- 2.7 Reducibility of submanifolds 27 -- 3 Submanifold geometry of orbits 33 -- 3.1 Isometric actions of Lie groups 34 -- 3.2 Polar actions and s-representations 41 -- 3.3 Equivariant maps 52 -- 3.4 Homogeneous submanifolds of Euclidean space 56 -- 3.5 Homogeneous submanifolds of hyperbolic spaces 58 -- 3.6 Second fundamental form of orbits 61 -- 3.7 Symmetric submanifolds 64 -- 3.8 Isoparametric hypersurfaces in space forms 81 -- 3.9 Algebraically constant second fundamental form 89 -- 4 The Normal Holonomy Theorem 95 -- 4.1 Normal holonomy".
catalog description "96 -- 4.2 The Normal Holonomy Theorem 106 -- 4.3 Proof of the Normal Holonomy Theorem 108 -- 4.4 Some geometric applications of the Normal Holonomy Theorem 116 -- 5 Isoparametric submanifolds and their focal manifolds 139 -- 5.1 Submersions and isoparametric maps 140 -- 5.2 Isoparametric submanifolds and Coxeter groups 143 -- 5.3 Geometric properties of submanifolds with constant principal curvatures 157 -- 5.4 Homogeneous isoparametric submanifolds 161 -- 5.5 Isoparametric rank 168 -- 6 Rank rigidity of submanifolds and normal holonomy of orbits 177 -- 6.1 Submanifolds with curvature normals of constant length and rank of homogeneous submanifolds 178 -- 6.2 Normal holonomy of orbits 191 -- 7 Homogeneous structures on submanifolds 201 -- 7.1 Homogeneous structures and homogeneity 202 -- 7.2 Examples of homogeneous structures 208 -- 7.3 Isoparametric submanifolds of higher rank 214 -- 8".
catalog description "Includes bibliographical references (p. 313-326) and index.".
catalog description "Submanifolds of Riemannian manifolds 223 -- 8.1 Submanifolds and the fundamental equations 224 -- 8.2 Focal points and Jacobi vector fields 225 -- 8.3 Totally geodesic submanifolds 230 -- 8.4 Totally umbilical submanifolds and extrinsic spheres 236 -- 8.5 Symmetric submanifolds 240 -- 9 Submanifolds of Symmetric Spaces 243 -- 9.1 Totally geodesic submanifolds 243 -- 9.2 Totally umbilical submanifolds and extrinsic spheres 252 -- 9.3 Symmetric submanifolds 256 -- 9.4 Submanifolds with parallel second fundamental form 266 -- 9.5 Homogeneous hypersurfaces 269 -- Appendix Basic material 281 -- A.1 Riemannian manifolds 281 -- A.2 Lie groups and Lie algebras 291 -- A.3 Homogeneous spaces 299 -- A.4 Symmetric spaces and flag manifolds 302.".
catalog extent "336 p. ;".
catalog identifier "1584883715 (alk. paper)".
catalog isPartOf "Chapman & Hall/CRC research notes in mathematics series ; 434.".
catalog isPartOf "Research notes in mathematics ; 434".
catalog issued "2003".
catalog issued "c2003.".
catalog language "eng".
catalog publisher "Boca Raton : Chapman & Hall/CRC,".
catalog subject "516.3/62 21".
catalog subject "Holonomy groups.".
catalog subject "QA649 .B467 2003".
catalog subject "Submanifolds.".
catalog tableOfContents "2 Basics of submanifold theory in space forms 7 -- 2.1 The fundamental equations for submanifolds of space forms 8 -- 2.2 Models of space forms 14 -- 2.3 Principal curvatures 17 -- 2.4 Totally geodesic submanifolds of space forms 20 -- 2.5 Reduction of the codimension 22 -- 2.6 Totally umbilical submanifolds of space forms 24 -- 2.7 Reducibility of submanifolds 27 -- 3 Submanifold geometry of orbits 33 -- 3.1 Isometric actions of Lie groups 34 -- 3.2 Polar actions and s-representations 41 -- 3.3 Equivariant maps 52 -- 3.4 Homogeneous submanifolds of Euclidean space 56 -- 3.5 Homogeneous submanifolds of hyperbolic spaces 58 -- 3.6 Second fundamental form of orbits 61 -- 3.7 Symmetric submanifolds 64 -- 3.8 Isoparametric hypersurfaces in space forms 81 -- 3.9 Algebraically constant second fundamental form 89 -- 4 The Normal Holonomy Theorem 95 -- 4.1 Normal holonomy".
catalog tableOfContents "96 -- 4.2 The Normal Holonomy Theorem 106 -- 4.3 Proof of the Normal Holonomy Theorem 108 -- 4.4 Some geometric applications of the Normal Holonomy Theorem 116 -- 5 Isoparametric submanifolds and their focal manifolds 139 -- 5.1 Submersions and isoparametric maps 140 -- 5.2 Isoparametric submanifolds and Coxeter groups 143 -- 5.3 Geometric properties of submanifolds with constant principal curvatures 157 -- 5.4 Homogeneous isoparametric submanifolds 161 -- 5.5 Isoparametric rank 168 -- 6 Rank rigidity of submanifolds and normal holonomy of orbits 177 -- 6.1 Submanifolds with curvature normals of constant length and rank of homogeneous submanifolds 178 -- 6.2 Normal holonomy of orbits 191 -- 7 Homogeneous structures on submanifolds 201 -- 7.1 Homogeneous structures and homogeneity 202 -- 7.2 Examples of homogeneous structures 208 -- 7.3 Isoparametric submanifolds of higher rank 214 -- 8".
catalog tableOfContents "Submanifolds of Riemannian manifolds 223 -- 8.1 Submanifolds and the fundamental equations 224 -- 8.2 Focal points and Jacobi vector fields 225 -- 8.3 Totally geodesic submanifolds 230 -- 8.4 Totally umbilical submanifolds and extrinsic spheres 236 -- 8.5 Symmetric submanifolds 240 -- 9 Submanifolds of Symmetric Spaces 243 -- 9.1 Totally geodesic submanifolds 243 -- 9.2 Totally umbilical submanifolds and extrinsic spheres 252 -- 9.3 Symmetric submanifolds 256 -- 9.4 Submanifolds with parallel second fundamental form 266 -- 9.5 Homogeneous hypersurfaces 269 -- Appendix Basic material 281 -- A.1 Riemannian manifolds 281 -- A.2 Lie groups and Lie algebras 291 -- A.3 Homogeneous spaces 299 -- A.4 Symmetric spaces and flag manifolds 302.".
catalog title "Submanifolds and holonomy / Jürgen Berndt, Sergio Console, and Carlos Olmos.".
catalog type "text".