Journal ArticleDOI
The automorphism groups of domains in complex space: a survey
TLDR
In this paper, the authors consider recent developments in the study of automorphism groups of domains in complex space and pay particular attention to results with a basis in geometry, and present a set of invariant metrics for complex differential geometry domains.Abstract:
We consider recent developments in the study of automorphism groups of domains in complex space. Particular attention is paid to results with a basis in geometry. Keywords: Domains, automorphism group, automorphism, invariant metrics, complex differential geometry Quaestiones Mathematicae 36(2013), 225–251read more
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Function theory in several complex variables
利雄 西野,Norman Levenberg,博史 山口 +2 more
TL;DR: The Poincare, Cousin, Runge, and Runge problems as discussed by the authors have been studied in the context of analytic spaces and pseudoconcave spaces, as well as holomorphic functions and analytic sets.
Journal ArticleDOI
Characterizing domains by the limit set of their automorphism group
TL;DR: In this paper, it was shown that the automorphism group of smoothly bounded convex domains is biholomorphic to a polynomial ellipsoid if and only if the limit set of the group intersects at least two closed complex faces of the set.
Book ChapterDOI
Semisimple Lie Algebras
TL;DR: This chapter considers a class of Lie algebras (the complex semisimple ones) that are sufficiently similar to sl(3; ℂ) that their representations can be described by a “theorem of the highest weight.”
Posted Content
On the automorphism groups of algebraic bounded domains
TL;DR: On the automorphism groups of algebraic bounded domains, see as mentioned in this paper for a discussion of the relation between bounded domains and algebraic automorphisms and bounded domains with bounded domains.
References
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Differential Geometry and Symmetric Spaces
TL;DR: In this article, the classification of symmetric spaces has been studied in the context of Lie groups and Lie algebras, and a list of notational conventions has been proposed.
Journal ArticleDOI
Real hypersurfaces in complex manifolds
TL;DR: In this paper, Cartan gave a complete solution of the equivalence problem, which is, among other results, the problem of finding a complete system of analytic invariants for two real analytic real hypersurfaees in Cn+l to be locally equivalent under biholomorphic transformations.
Book
Differential analysis on complex manifolds
TL;DR: In this paper, the authors present an introduction to the basics of analysis and geometry on compact complex manifolds and provide tools which are the building blocks of many mathematical developments over the past 30 years.
Related Papers (5)
Characterization of Reinhardt domains by their automorphism groups
Alexander Isaev,Steven G. Krantz +1 more