## Geometry of Cauchy-Riemann SubmanifoldsSorin Dragomir, Mohammad Hasan Shahid, Falleh R. Al-Solamy This book gathers contributions by respected experts on the theory of isometric immersions between Riemannian manifolds, and focuses on the geometry of CR structures on submanifolds in Hermitian manifolds. CR structures are a bundle theoretic recast of the tangential Cauchy–Riemann equations in complex analysis involving several complex variables. The book covers a wide range of topics such as Sasakian geometry, Kaehler and locally conformal Kaehler geometry, the tangential CR equations, Lorentzian geometry, holomorphic statistical manifolds, and paraquaternionic CR submanifolds. Intended as a tribute to Professor Aurel Bejancu, who discovered the notion of a CR submanifold of a Hermitian manifold in 1978, the book provides an up-to-date overview of several topics in the geometry of CR submanifolds. Presenting detailed information on the most recent advances in the area, it represents a useful resource for mathematicians and physicists alike. |

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### Contents

1 | |

2 CRSubmanifolds and δInvariants | 27 |

3 CRSubmanifolds of the Nearly Kähler 6Sphere | 56 |

4 CR Submanifolds of Hermitian Manifolds and the Tangential CR Equations | 91 |

5 CR Submanifolds in lca Kaehler and Smanifolds | 123 |

6 Lorentzian Geometry and CRSubmanifolds | 151 |

7 Submanifold Theory in Holomorphic Statistical Manifolds | 179 |

8 CRSubmanifolds in Complex and Sasakian Space Forms | 216 |

9 CRDoubly Warped Product Submanifolds | 267 |

10 Ideal CR Submanifolds | 289 |

11 Submersions of CR Submanifolds | 311 |

12 CRSubmanifolds of SemiRiemannian Kaehler Manifolds | 343 |

13 Paraquaternionic CRSubmanifolds | 361 |

### Other editions - View all

Geometry of Cauchy-Riemann Submanifolds Sorin Dragomir,Mohammad Hasan Shahid,Falleh R. Al-Solamy No preview available - 2016 |

### Common terms and phrases

anti-invariant Bejancu Cauchy–Riemann Chen complex space form complex structure constant holomorphic sectional contact CR contact CR-submanifolds CR function CR manifold CR-product CR-submanifold CR-warped product CR–Lorentzian curvature tensor defined Definition denote dimensional equality sign equation f-structure formulas Gauss Geom geometry Hermitian manifold holds identically holomorphic sectional curvature holomorphic statistical manifold hypersurface inequality integrable invariant submanifold isometric immersion Kaehler manifold Lemma Levi-Civita connection lightlike Lorentzian Math mean curvature metric g minimal mixed foliate mixed totally geodesic n-dimensional normal bundle orthogonal orthonormal frame product CR-submanifolds Proof real hypersurface real space form resp respectively Riemannian manifold Sasakian manifold Sasakian space form satisfies the equality second fundamental form sectional curvature semi-Riemannian shape operator spacelike subspace tangent to M1 tensor field Theorem timelike totally geodesic totally real submanifold totally umbilical vector field warped product warped product submanifold