Minimal Submanifolds in Pseudo-Riemannian Geometry by HENRI Anciaux, Hardcover | Indigo Chapters

Since the foundational work of Lagrange on the differential equation to be satisfied by a minimal surface of the Euclidean space, the theory of minimal submanifolds have undergone considerable developments, involving techniques from related areas, such as the analysis of partial differential equations and complex analysis. On the other hand, the relativity theory has led to the study of pseudo-Riemannian manifolds, which turns out to be the most general framework for the study of minimal submanifolds. However, most of the recent books on the subject still present the theory only in the Riemannian case. For the first time, this book provides a self-contained and accessible introduction to the subject in the general setting of pseudo-Riemannian geometry, only assuming from the reader some basic knowledge about manifold theory. Several classical results, such as the Weierstrass representation formula for minimal surfaces, and the minimizing properties of complex submanifolds, are presented in full generality without sacrificing the clarity of exposition. Contents: Submanifolds in Pseudo-Riemannian Geometry; Minimal Surfaces in Pseudo-Euclidean Space; Equivariant Minimal Hypersurfaces in Space Forms; Pseudo-Kahler Manifolds; Complex and Lagrangian Submanifolds in Pseudo-Kahler Manifolds & Minimizing Properties of Minimal Submanifolds. | Minimal Submanifolds in Pseudo-Riemannian Geometry by HENRI Anciaux, Hardcover | Indigo Chapters