Eveline Legendre

Existence and non-uniqueness of constant scalar curvature toric Sasaki metrics

We study compatible toric Sasaki metrics with constant scalar curvature on co-oriented compact toric contact manifolds of Reeb type of dimension at least 5. These metrics come in rays of transversal homothety due to the possible rescaling of the Reeb vector fields. We prove that there exist Reeb vector fields for which the transversal Futaki invariant (restricted to the Lie algebra of the torus) vanishes. Using existence result of [25], we show that a co-oriented compact toric contact 5-manifold whose moment cone has 4 facets admits a finite number of rays of transversal homothetic compatible toric Sasaki metrics with constant scalar curvature. We point out a family of well-known toric contact structures on

Toric Contact Geometry in Arbitrary Codimension

S^2\times S^3

Toric Aspects of the First Eigenvalue

admitting two non isometric and non transversally homothetic compatible toric Sasaki metrics with constant scalar curvature.

Toric Kähler–Einstein Metrics and Convex Compact Polytopes

We define toric contact manifolds in arbitrary codimension and give a description of such manifolds in terms of a kind of labelled polytope embedded into a grassmannian, analogous to the Delzant polytope of a toric symplectic manifold.

The Einstein–Hilbert Functional and the Sasaki–Futaki Invariant

In this paper we study the smallest non-zero eigenvalue

Toric generalized Kähler–Ricci solitons with Hamiltonian 2-form

\lambda _1

Reducibility in Sasakian geometry

λ1 of the Laplacian on toric Kähler manifolds. We find an explicit upper bound for