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 ⊆ 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 G ¯ of dimension three, when G is unimodular and 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 α di foliazioni su varietà riemanniane e si ottiene una formula per il laplaciano ∇ 2 ⁡ α - 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 .