On Ricci Negative Lie Groups

Lauret, Jorge; Will, Cynthia E.

doi:10.1007/978-3-030-81296-6_9

Cited by 5 publications

(3 citation statements)

References 32 publications

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“…•, • (see the recent surveys [L3,LW] and the references therein for further information on this viewpoint).…”

Section: Preliminariesmentioning

confidence: 99%

Prescribing Ricci curvature on homogeneous spaces

Lauret¹,

Will²

2020

Preprint

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The prescribed Ricci curvature problem in the context of G-invariant metrics on a homogeneous space M = G/K is studied. We focus on the metrics at which the map g → Rc(g) is, locally, as injective and surjective as it can be. Our main result is that such property is generic in the compact case. Our main tool is a formula for the Lichnerowicz Laplacian we prove in terms of the moment map for the variety of algebras.

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“…•, • (see the recent surveys [L3,LW] and the references therein for further information on this viewpoint).…”

Section: Preliminariesmentioning

confidence: 99%

Prescribing Ricci curvature on homogeneous spaces

Lauret¹,

Will²

2020

Preprint

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“…The moving-bracket approach has actually been used for decades in homogeneous geometry (see the overviews given in [L8, Section 5] and [LW2,Section 3]). In most applications, concepts and results from geometric invariant theory, including moment maps and their convexity properties, closed orbits, stability, categorical quotients and Kirwan stratification, have been exploited in one way or another.…”

Section: The Moving-bracket Approachmentioning

confidence: 99%

The search for solitons on homogeneous spaces

Lauret¹

2019

Preprint

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The concept of soliton, in its most general version, allows us to find canonical or distinguished elements on any set provided with an equivalence relation and an 'optimal' tangent direction at each point. We study in this paper solitons on homogeneous spaces, which have consolidated its role as a quite useful tool to find soliton geometric structures in Riemannian, pseudo-Riemannian, complex, symplectic and G2 geometries.

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“…As an application, we obtain that any nilpotent Lie algebra of dimension 7 having a non-nilpotent derivation is a RN-nilradical (see Theorem 3.19). More applications are developed in the forthcoming paper [LW2].…”

Section: Introductionmentioning

confidence: 99%

On Ricci negative solvmanifolds and their nilradicals

Deré

Lauret

2019

Mathematische Nachrichten

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In the homogeneous case, the only curvature behavior which is still far from being understood is Ricci negative. In this paper, we study which nilpotent Lie algebras admit a Ricci negative solvable extension. Different unexpected behaviors were found. On the other hand, given a nilpotent Lie algebra, we consider the space of all the derivations such that the corresponding solvable extension has a metric with negative Ricci curvature. Using the nice convexity properties of the moment map for the variety of nilpotent Lie algebras, we obtain a useful characterization of such derivations and some applications. K E Y W O R D S negative, Ricci, solvmanifold M S C ( 2 0 1 0 ) 53C20, 53C30 1462

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On Ricci Negative Lie Groups

Cited by 5 publications

References 32 publications

Prescribing Ricci curvature on homogeneous spaces

Prescribing Ricci curvature on homogeneous spaces

The search for solitons on homogeneous spaces

On Ricci negative solvmanifolds and their nilradicals

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