Geometry of Cauchy-Riemann Submanifolds

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. Front Matter....Pages i-xviii CR-Warped Submanifolds in Kaehler Manifolds....Pages 1-25 CR-Submanifolds and \(\delta \) -Invariants....Pages 27-55 CR-Submanifolds of the Nearly Kähler 6-Sphere....Pages 57-90 CR Submanifolds of Hermitian Manifolds and the Tangential CR Equations....Pages 91-122 CR Submanifolds in (l.c.a.) Kaehler and S-manifolds....Pages 123-150 Lorentzian Geometry and CR-Submanifolds....Pages 151-177 Submanifold Theory in Holomorphic Statistical Manifolds....Pages 179-215 CR-Submanifolds in Complex and Sasakian Space Forms....Pages 217-266 CR-Doubly Warped Product Submanifolds....Pages 267-288 Ideal CR Submanifolds....Pages 289-310 Submersions of CR Submanifolds....Pages 311-342 CR-Submanifolds of Semi-Riemannian Kaehler Manifolds....Pages 343-359 Paraquaternionic CR-Submanifolds....Pages 361-390