Ricci curvature in the neighborhood of rank-one symmetric spaces

  title={Ricci curvature in the neighborhood of rank-one symmetric spaces},
  author={Erwann Delay and Marc Herzlich},
  journal={The Journal of Geometric Analysis},
We study the Ricci curvature of a Riemannian metric as a differential operator acting on the space of metrics close (in a weighted functional spaces topology) to the standard metric of a rank-one noncompact symmetric space. We prove that any symmetric bilinear field close enough to the standard may be realized as the Ricci curvature of a unique close metric if its decay rate at infinity (its weight) belongs to some precisely known interval. We also study what happens if the decay rate is too… 

^{} almost conformal isometries of Sub-Semi-Riemannian metrics and solvability of a Ricci equation

Let M be a smooth compact manifold without boundary. We consider two smooth Sub-Semi-Riemannian metrics on M. Under suitable conditions, we show that they are almost conformally isometric in an Lp

Studies of Some Curvature Operators in a Neighborhood of an Asymptotically Hyperbolic Einstein Manifold

Abstract On an asymptotically hyperbolic Einstein manifold ( M , g 0 ) for which the Yamabe invariant of the conformal structure on the boundary at infinity is nonnegative, we show that the operators

Inversion of some curvature operators near a parallel Ricci metric II: Non-compact manifold with bounded geometry

Let (M,g) be a complete noncompact riemannian manifold with bounded geometry and parallel Ricci curvature. We show that some operators, "affine" relatively to the Ricci curvature, are locally

Local stability of Einstein metrics under the Ricci iteration

The prescribed Ricci curvature problem on three‐dimensional unimodular Lie groups

Let G be a three‐dimensional unimodular Lie group, and let T be a left‐invariant symmetric (0,2)‐tensor field on G. We provide the necessary and sufficient conditions on T for the existence of a pair

Prescribing Ricci curvature on a product of spheres

We prove an existence result for the prescribed Ricci curvature equation for certain doubly warped product metrics on $$\mathbb {S}^{d_1+1}\times \mathbb {S}^{d_2}$$ S d 1 + 1 × S d 2 , where $$d_i

Maxima of Curvature Functionals and the Prescribed Ricci Curvature Problem on Homogeneous Spaces

  • A. Pulemotov
  • Mathematics
    The Journal of Geometric Analysis
  • 2019
Consider a compact Lie group G and a closed Lie subgroup $$H<G$$ H < G . Let $${\mathcal {M}}$$ M be the set of G -invariant Riemannian metrics on the homogeneous space $$M=G/H$$ M = G / H . By

TT-eigentensors for the Lichnerowicz Laplacian on some asymptotically hyperbolic manifolds with warped products metrics

Let (M =]0, ∞[×N, g) be an asymptotically hyperbolic manifold of dimension n +  1 ≥  3, equipped with a warped product metric. We show that there exist no TT L2-eigentensors with eigenvalue in the

Fredholm Operators and Einstein Metrics on Conformally Compact Manifolds

The main purpose of this monograph is to give an elementary and self-contained account of the existence of asymptotically hyperbolic Einstein metrics with prescribed conformal infinities sufficiently

A Burns-Epstein invariant for ACHE 4-manifolds

We define a renormalized characteristic class for Einstein asymptotically complex hyperbolic (ACHE) manifolds of dimension 4: for any such manifold, the polynomial in the curvature associated to the



The Dirichlet problem at infinity for manifolds of negative curvature

On considere l'existence de fonctions harmoniques bornees sur des varietes simplement connexes N n de courbure negative

Representation Theory: A First Course

This volume represents a series of lectures which aims to introduce the beginner to the finite dimensional representations of Lie groups and Lie algebras. Following an introduction to representation

Analyse précisée d'équations semi-linéaires elliptiques sur l'espace hyperbolique et application à la courbure scalaire conforme

Au theme de la courbure scalaire conforme sur l'espace hyperbolique nous apportons ici une etude fine du comportement asymptotique en toute dimension. Nous traitons toujours d'equations

The Ricci Curvature Equation

Let g = {gij be a Riemannian metric on a manifold M of dimension n. It is Ricci curvature Rc(g) = {Rij} is given by the formula $$ {R_{{ij}}} = \frac{1}{{2(n - 1)}}{g^{{k2}}}\left[

Riemannian geometry and holonomy groups

Weak holonomy in dimension 16, Preprint Humboldt-Univ

  • Weak holonomy in dimension 16, Preprint Humboldt-Univ
  • 1999

Département de Mathématiques, Université de Tours (Laboratoire de mathématiques et physique théorique, UPRESA 6083 du CNRS)

  • Département de Mathématiques, Université de Tours (Laboratoire de mathématiques et physique théorique, UPRESA 6083 du CNRS)