A differential geometric characterization of invariant domains of holomorphy

Gregor Fels

Displaying similar documents to “A differential geometric characterization of invariant domains of holomorphy”

On the complex geometry of invariant domains in complexified symmetric spaces

Karl-Hermann Neeb (1999)

Annales de l'institut Fourier

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Let $M = G / H$ be a real symmetric space and $𝔤 = 𝔥 + 𝔮$ the corresponding decomposition of the Lie algebra. To each open $H$ -invariant domain $D_{𝔮} \subseteq i 𝔮$ consisting of real ad-diagonalizable elements, we associate a complex manifold $Ξ (D_{𝔮})$ which is a curved analog of a tube domain with base $D_{𝔮}$ , and we have a natural action of $G$ by holomorphic mappings. We show that $Ξ (D_{𝔮})$ is a Stein manifold if and only if $D_{𝔮}$ is convex, that the envelope of holomorphy is schlicht and that $G$ -invariant plurisubharmonic functions correspond to...

Comparison of metrics on three-dimensional Lie groups

Federico G. Lastaria (1991)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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We study local equivalence of left-invariant metrics with the same curvature on Lie groups $G$ and $\bar{G}$ of dimension three, when $G$ is unimodular and $\bar{G}$ is non-unimodular.

On the geometrical properties of Heisenberg groups

Mehri Nasehi (2020)

Archivum Mathematicum

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In [20] the existence of major differences about totally geodesic two-dimensional foliations between Riemannian and Lorentzian geometry of the Heisenberg group $H_{3}$ is proved. Our aim in this paper is to obtain a comparison on some other geometrical properties of these spaces. Interesting behaviours are found. Also the non-existence of left-invariant Ricci and Yamabe solitons and the existence of algebraic Ricci soliton in both Riemannian and Lorentzian cases are proved. Moreover, all of...

On naturally reductive left-invariant metrics of $SL (2, ℝ)$

Stefan Halverscheid, Andrea Iannuzzi (2006)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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On any real semisimple Lie group we consider a one-parameter family of left-invariant naturally reductive metrics. Their geodesic flow in terms of Killing curves, the Levi Civita connection and the main curvature properties are explicitly computed. Furthermore we present a group theoretical revisitation of a classical realization of all simply connected 3-dimensional manifolds with a transitive group of isometries due to L. Bianchi and É. Cartan. As a consequence one obtains a characterization...

A Weitzenbôck formula for the second fundamental form of a Riemannian foliation

Paolo Piccinni (1984)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Si considera la seconda forma fondamentale $\alpha$ di foliazioni su varietà riemanniane e si ottiene una formula per il laplaciano $\nabla^{2}\alpha$ - Se ne deducono alcune implicazioni per foliazioni su varietà a curvatura costante.

Complex structures on $S O_{g} (M)$

Tommaso Pacini (1999)

Bollettino dell'Unione Matematica Italiana

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Data una varietà Riemanniana orientata $(M, g)$ , il fibrato principale $S O_{g} (M)$ di basi ortonormali positive su $(M, g)$ ha una parallelizzazione canonica dipendente dalla connessione di Levi-Civita. Questo fatto suggerisce la definizione di una classe molto naturale di strutture quasi-complesse su $(M, g)$ . Dopo le necessarie definizioni, discutiamo qui l'integrabilità di queste strutture, esprimendola in termini della struttura Riemanniana $g$ .

Addition to the paper “Translation invariant subspaces of $L_{p} (G)$ ” Studia Mathematica 48 (1973), pp. 245-250

Aharon Atzmon (1975)

Studia Mathematica

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Displaying similar documents to “A differential geometric characterization of invariant domains of holomorphy”

On the complex geometry of invariant domains in complexified symmetric spaces

Comparison of metrics on three-dimensional Lie groups

On the geometrical properties of Heisenberg groups

On naturally reductive left-invariant metrics of SL ( 2 , ℝ )

A Weitzenbôck formula for the second fundamental form of a Riemannian foliation

Complex structures on S ⁢ O g ⁢ M

Addition to the paper “Translation invariant subspaces of L p ( G ) ” Studia Mathematica 48 (1973), pp. 245-250

On naturally reductive left-invariant metrics of $SL (2, ℝ)$

Complex structures on $S O_{g} (M)$

Addition to the paper “Translation invariant subspaces of $L_{p} (G)$ ” Studia Mathematica 48 (1973), pp. 245-250