Geometry of Cauchy-Riemann Submanifolds

Dragomir, Sorin (EDT)/ Shahid, Mohammad Hasan (EDT)/ Al-Solamy, Falleh R. (EDT)

Springer Verlag, Singapore（2018/06発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 390 p.
• 言語 ENG
• 商品コード 9789811092831
• DDC分類 516.1

Full Description

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.

Contents

Chapter 1. CR-warped submanifolds in Kaehler manifolds.- Chapter 2. CR Submanifolds and -invariants.- Chapter 3. CR Submanifolds of the nearly Kahler 6-sphere.- Chapter 4. CR submanifolds of Hermitian manifolds and the tangential C-R equations.- Chapter 5. CR Submanifolds in (l.c.a.) Kaehler and S-manifolds.- Chapter 6. Lorentzian geometry and CR submanifolds.- Chapter 7. Submanifolds in holomorphic statistical manifolds.- Chapter 8. CR Submanifolds in complex and Sasakian space forms.- Chapter 9. CR-Doubly warped product submanifolds.- Chapter 10. Ideal CR submanifolds.- Chapter 11. Submersions of CR submanifolds.- Chapter 12. CR Submanifolds of semi-Kaehler manifolds.- Chapter 13. Paraquaternionic CR submanifolds.