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. Finally, a number of very recent results on the subject, including the classification of equivariant minimal hypersurfaces in pseudo-Riemannian space forms and the characterization of minimal Lagrangian surfaces in some pseudo-Kaehler manifolds are given.
Sprache
Verlagsort
Zielgruppe
Für höhere Schule und Studium
Für Beruf und Forschung
Graduate and PhD students in differential geometry and related fields; researchers in differential geometry and related fields; theoretical physicists.
Maße
Höhe: 235 mm
Breite: 157 mm
Dicke: 15 mm
Gewicht
ISBN-13
978-981-4291-24-8 (9789814291248)
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Schweitzer Klassifikation
Autor*in
Univ Of Sao Paulo, Brazil
Pseudo-Riemannian Manifolds; Submanifolds; First and Second Variations of Volume; Minimal Submanifolds; Simple Examples of Minimal Surfaces; Weierstrass Representation Formulas for Spacelike and Timelike Minimal Surface in Euclidean Space of Arbitrary Dimension; Equivariant Minimal Hypersurfaces in Space Forms; Pseudo-Kahler Manifolds; Complex and Lagrangian Submanifolds; Examples of Minimal Lagrangian Submanifolds.