In this paper, we compute Riemannian metrics on the Siegel-Jacobi space which are invariant under the natural action of the Jacobi group explicitly and also provide the Laplacians of these invariant metrics. These are expressed in terms of the trace form.

In this paper, we compute Riemannian metrics on the Siegel-Jacobi space which are invariant under the natural action of the Jacobi group explicitly and also provide the Laplacians of these invariant metrics. These are expressed in terms of the trace form.

The subject of left-invariant Ricci soliton metrics on nilpotent Lie groups has enjoyed quite a bit of attention in the past several years. These metrics are intimately related to left-invariant Einstein metrics on non-unimodular solvable Lie groups. In fact, a classification of one is equivalent to a classification of the other. In this note, we focus our attention on nilpotent Lie groups and ...

New features of the generalized symmetries of generic two-dimensional dilaton models of gravity are presented and invariant gravity-matter couplings are introduced. We show that there is a continuum set of Noether symmetries, which contains half a de Witt algebra. Two of these symmetries are area-preserving transformations. We show that gravity-matter couplings which are invariant under area pr...

A left invariant metric on a nilpotent Lie group is called minimal, if it minimizes the norm of the Ricci tensor among all left invariant metrics with the same scalar curvature. Such metrics are unique up to isometry and scaling and the groups admitting a minimal metric are precisely the nilradicals of (standard) Einstein solvmanifolds. If N is endowed with an invariant symplectic, complex or h...

New features of the generalized symmetries of generic two-dimensional dilaton models of gravity are presented and invariant gravity-matter couplings are introduced. We show that there is a continuum set of Noether symmetries, which contains half a de Witt algebra. Two of these symmetries are area-preserving transformations. We show that gravity-matter couplings which are invariant under area pr...

New features of the generalized symmetries of generic two-dimensional dilaton models of gravity are presented and invariant gravity-matter couplings are introduced. We show that there is a continuum set of Noether symmetries, which contents a de Witt algebra. Two of these symmetries are area-preserving transformations. We show that gravity-matter couplings which are invariant under area preserv...

The Yamabe invariant Y(M) of a smooth compact manifold is roughly the supremum of the scalar curvatures of unit-volume constant-scalarcurvature Riemannian metrics g on M . (To be precise, one only considers those constant-scalar-curvature metrics which are Yamabe minimizers, but this technicality does not, e.g., affect the sign of the answer.) In this article, it is shown that many 4-manifolds ...