Torsion and critical metrics on contact three-manifolds

Domenico Perrone

doi:10.2996/kmj/1138039163

Abstract

Torsion and critical metrics on contact three-manifolds

Highlights

Let M be a compact orientable manifold of class C°°
Riemannian three-manifold (M, ω, g) with g critical metric of βc The main purpose of this paper is to study compact Riemannian threemanifolds (M, ω, g) with g critical metric of the functional £F
We show that the metric of a compact contact Riemannian three-manifold (M, ω, g, X0) whose characteristic vector field X0 is of Killing, may be deformed to a contact metric of positive sectional curvature if either the Ricci curvature is greater than —2g or the ^-sectional curvature is greater than —3

Summary

Introduction

Let M be a compact orientable manifold of class C°°. It is well known that a Riemannian metric g on M is a critical point of the functional "integral of the scalar curvature \ rdv" defined on the set of all Riemannian metrics of the same total volume on M, if and only if g is an Einstein metric. let (M, ω) be a compact contact three-manifold. Let (ω, g) be a contact Riemannian structure on a compact three-manifold M. ( i ) Note that : M is /Γ-contact if and only if g is a critical metric for

Objectives

Results

Conclusion