Falleh R. Al-Solamy – författare

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.

This book, Differential Geometry: Riemannian Geometry and Isometric Immersions (Book I-B), is the first in a captivating series of four books presenting a choice of topics, among fundamental and more advanced in differential geometry (DG). Starting with the basics of semi-Riemannian geometry, the book aims to develop the understanding of smooth 1-parameter variations of geodesics of, and correspondingly of, Jacobi fields. A few algebraic aspects required by the treatment of the Riemann–Christoffel four-tensor and sectional curvature are successively presented. Ricci curvature and Einstein manifolds are briefly discussed. The Sasaki metric on the total space of the tangent bundle over a Riemannian manifold is built, and its main properties are investigated. An important integration technique on a Riemannian manifold, related to the geometry of geodesics, is presented for further applications. The other three books of the series are

Differential Geometry 1: Manifolds, Bundle and Characteristic Classes (Book I-A)Differential Geometry 3: Foundations of Cauchy-Riemann and Pseudohermitian Geometry (Book I-C)Differential Geometry 4: Advanced Topics in Cauchy–Riemann and Pseudohermitian Geometry (Book I-D)

The four books belong to a larger book project (Differential Geometry, Partial Differential Equations, and Mathematical Physics) by the same authors, aiming to demonstrate how certain portions of DG and the theory of partial differential equations apply to general relativity and (quantum) gravity theory. These books supply some of the ad hoc DG machinery yet do not constitute a comprehensive treatise on DG, but rather authors’ choice based on their scientific (mathematical and physical) interests. These are centered around the theory of immersions—isometric, holomorphic, Cauchy–Riemann (CR)—and pseudohermitian geometry, as devised by Sidney Martin Webster for the study of nondegenerate CR structures, themselves a DG manifestation of the tangential CR equations.

This book, Differential Geometry: Manifolds, Bundles and Characteristic Classes (Book I-A), is the first in a captivating series of four books presenting a choice of topics, among fundamental and more advanced, in differential geometry (DG), such as manifolds and tensor calculus, differentiable actions and principal bundles, parallel displacement and exponential mappings, holonomy, complex line bundles and characteristic classes. The inclusion of an appendix on a few elements of algebraic topology provides a didactical guide towards the more advanced Algebraic Topology literature. The subsequent three books of the series are:

Differential Geometry: Riemannian Geometry and Isometric Immersions (Book I-B)

Differential Geometry: Foundations of Cauchy-Riemann and Pseudohermitian Geometry (Book I-C)

Differential Geometry: Advanced Topics in Cauchy–Riemann and Pseudohermitian Geometry (Book I-D)

The four books belong to an ampler book project (Differential Geometry, Partial Differential Equations, and Mathematical Physics, by the same authors) and aim to demonstrate how certain portions of DG and the theory of partial differential equations apply to general relativity and (quantum) gravity theory. These books supply some of the ad hoc DG machinery yet do not constitute a comprehensive treatise on DG, but rather Authors’ choice based on their scientific (mathematical and physical) interests. These are centered around the theory of immersions - isometric, holomorphic, and Cauchy-Riemann (CR) -and pseudohermitian geometry, as devised by Sidney Martin Webster for the study of nondegenerate CR structures, themselves a DG manifestation of the tangential CR equations.