Progress in Mathematics

By: Kentaro Yano, Masahiro Kon

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Paperback | 14 June 2012

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226 Pages

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I. Structures on Riemannian manifolds.- x1. Riemannian manifolds.- x2. Kaehlerian manifolds.- x3. Sasakian manifolds.- x4. f-structure.- II. Submanifolds.- x1. Induced connection and second fundamental form.- x2. Equations of Gauss, Codazzi and Ricci.- x3. Normal connection.- x4. Laplacian of the second fundamental form.- x5. Submanifolds of space forms.- x6. Parallel second fundamental form.- III. Contact CR submanifolds.- x1. Submanifolds of Sasakian manifolds.- x2. f-structure on submanifolds.- x3. Integrability of distributions.- x4. Totally contact umbilical submanifolds.- x5. Examples of contact CR submanifolds.- x6. Flat normal connection.- x7. Minimal contact CR submanifolds.- IV. CR submanifolds.- x1. Submanifolds of Kaehlerian manifolds.- x2. CR submanifolds of Hermitian manifolds.- x3. Characterization of CR submanifolds.- x4. Distributions.- x5. Parallel f-structure.- x6. Totally umbilical submanifolds.- x7. Examples of CR submanifolds.- x8. Semi-flat normal connection.- x9. Normal connection of invariant submanifolds.- x10. Parallel mean curvature vector.- x11. Integral formulas.- x12. CR submanifolds of Cm.- V. Submanifolds and Riemannian fibre bundles.- x1. Curvature tensors.- x2. Mean curvature vector.- x3. Lengths of the second fundamental forms.- VI. Hypersurfaces.- x1. Real hypersurfaces of complex space forms.- x2. Pseudo-Einstein real hypersurfaces.- x3. Generic minimal submanifolds.- x4. Semidefinite second fundamental form.- x5. Hypersurfaces of S2n+1.- x6. (f,g,u,v,?)-structure.- Author index.

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