CR Submanifolds of Kaehlerian and Sasakian Manifolds

Inhaltsverzeichnis

• I. Structures on Riemannian manifolds.
• §1. Riemannian manifolds.
• §2. Kaehlerian manifolds.
• §3. Sasakian manifolds.
• §4. f-structure.
• II. Submanifolds.
• §1. Induced connection and second fundamental form.
• §2. Equations of Gauss, Codazzi and Ricci.
• §3. Normal connection.
• §4. Laplacian of the second fundamental form.
• §5. Submanifolds of space forms.
• §6. Parallel second fundamental form.
• III. Contact CR submanifolds.
• §1. Submanifolds of Sasakian manifolds.
• §2. f-structure on submanifolds.
• §3. Integrability of distributions.
• §4. Totally contact umbilical submanifolds.
• §5. Examples of contact CR submanifolds.
• §6. Flat normal connection.
• §7. Minimal contact CR submanifolds.
• IV. CR submanifolds.
• §1. Submanifolds of Kaehlerian manifolds.
• §2. CR submanifolds of Hermitian manifolds.
• §3. Characterization of CR submanifolds.
• §4. Distributions.
• §5. Parallel f-structure.
• §6. Totally umbilical submanifolds.
• §7. Examples of CR submanifolds.
• §8. Semi-flat normal connection.
• §9. Normal connection of invariant submanifolds.
• §10. Parallel mean curvature vector.
• §11. Integral formulas.
• §12. CR submanifolds of Cm.
• V. Submanifolds and Riemannian fibre bundles.
• §1. Curvature tensors.
• §2. Mean curvature vector.
• §3. Lengths of the second fundamental forms.
• VI. Hypersurfaces.
• §1. Real hypersurfaces of complex space forms.
• §2. Pseudo-Einstein real hypersurfaces.
• §3. Generic minimal submanifolds.
• §4. Semidefinite second fundamental form.
• §5. Hypersurfaces of S2n+1.
• §6. (f, g, u, v,?)-structure.
• Author index.