Displaying similar documents to “Spectral isolation of bi-invariant metrics on compact Lie groups”

The second Yamabe invariant with singularities

Mohammed Benalili, Hichem Boughazi (2012)

Annales mathématiques Blaise Pascal

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Let ( M , g ) be a compact Riemannian manifold of dimension n ≥ 3 .We suppose that g is a metric in the Sobolev space H 2 p ( M , T * M ⊗ T * M ) with p > n 2 and there exist a point P ∈ M and δ > 0 such that g is smooth in the ball B p ( δ ) . We define the second Yamabe invariant with singularities as the infimum of the second eigenvalue of the singular Yamabe operator over a generalized class of conformal metrics to g and of volume 1 . We show that this operator is attained by a generalized metric, we deduce nodal solutions to a Yamabe type equation...

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...

Ricci-flat left-invariant Lorentzian metrics on 2-step nilpotent Lie groups

Mohammed Guediri, Mona Bin-Asfour (2014)

Archivum Mathematicum

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The purpose of this paper is to investigate Ricci-flatness of left-invariant Lorentzian metrics on 2-step nilpotent Lie groups. We first show that if , is a Ricci-flat left-invariant Lorentzian metric on a 2-step nilpotent Lie group N , then the restriction of , to the center of the Lie algebra of N is degenerate. We then characterize the 2-step nilpotent Lie groups which can be endowed with a Ricci-flat left-invariant Lorentzian metric, and we deduce from this that a Heisenberg Lie group...