On completeness of left-invariant Lorentz metrics on solvable Lie groups.

Mohammed Guediri

Displaying similar documents to “On completeness of left-invariant Lorentz metrics on solvable Lie groups.”

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...

Lie groups with no left invariant complex structures

Cordero, Luis A., Fernández, Marisa, Gray, Alfred (1990)

Portugaliae mathematica

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Spectral isolation of bi-invariant metrics on compact Lie groups

Carolyn S. Gordon, Dorothee Schueth, Craig J. Sutton (2010)

Annales de l’institut Fourier

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We show that a bi-invariant metric on a compact connected Lie group $G$ is spectrally isolated within the class of left-invariant metrics. In fact, we prove that given a bi-invariant metric $g_{0}$ on $G$ there is a positive integer $N$ such that, within a neighborhood of $g_{0}$ in the class of left-invariant metrics of at most the same volume, $g_{0}$ is uniquely determined by the first $N$ distinct non-zero eigenvalues of its Laplacian (ignoring multiplicities). In the case where $G$ is simple, $N$ can be chosen...