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The study of CR manifolds lies at the intersection of three main mathematical disciplines: partial differential equations, complex analysis in several complex variables, and differential geometry. While the PDE and complex analytic aspects have been intensely studied in the last fifty years, much effort has recently been made to understand the differential geometric side of the subject. This monograph provides a unified presentation of several differential geometric aspects in the theory of CR manifolds and tangential Cauchy–Riemann equations. It presents the major differential geometric achievements in the theory of CR manifolds, such as the Tanaka–Webster connection, Fefferman's metric, pseudo-Einstein structures and the Lee conjecture, CR immersions, subelliptic harmonic maps as a local manifestation of pseudoharmonic maps from a CR manifold, Yang–Mills fields on CR manifolds, to name a few. It also aims at explaining how certain results from analysis are employed in CR geometry. Motivated by clear exposition, many examples, explicitly worked-out geometric results, and stimulating unproved statements and comments referring to the most recent aspects of the theory, this monograph is suitable for researchers and graduate students in differential geometry, complex analysis, and PDEs.

Geometry, Differential. --- CR submanifolds. --- Differentiable manifolds. --- Differential manifolds --- Manifolds (Mathematics) --- Cauchy-Riemann submanifolds --- Submanifolds, CR --- Differential geometry --- CR submanifolds --- Differentiable manifolds --- Geometry, Differential --- Global differential geometry. --- Global analysis. --- Differential equations, partial. --- Global analysis (Mathematics). --- Differential Geometry. --- Global Analysis and Analysis on Manifolds. --- Partial Differential Equations. --- Several Complex Variables and Analytic Spaces. --- Analysis. --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Partial differential equations --- Differential geometry. --- Manifolds (Mathematics). --- Partial differential equations. --- Functions of complex variables. --- Mathematical analysis. --- Analysis (Mathematics). --- 517.1 Mathematical analysis --- Mathematical analysis --- Complex variables --- Elliptic functions --- Functions of real variables --- Topology

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Differential geometry. Global analysis --- Analytical spaces --- Partial differential equations --- Mathematical analysis --- differentiaalvergelijkingen --- analyse (wiskunde) --- differentiaal geometrie

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Geometry, Differential --- Kählerian manifolds

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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.

Differential geometry. Global analysis --- Geometry --- Discrete mathematics --- Mathematics --- Mathematical physics --- Geology. Earth sciences --- differentiaal geometrie --- discrete wiskunde --- wiskunde --- fysica --- geofysica --- geometrie