Displaying similar documents to “Metrics conformally equivalent to bounded geometry”

Jet isomorphism for conformal geometry

Robin C. Graham (2007)

Archivum Mathematicum

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Jet isomorphism theorems for conformal geometry are discussed. A new proof of the jet isomorphism theorem for odd-dimensional conformal geometry is outlined, using an ambient realization of the conformal deformation complex. An infinite order ambient lift for conformal densities in the case in which harmonic extension is obstructed is described. A jet isomorphism theorem for even dimensional conformal geometry is formulated using the inhomogeneous ambient metrics recently introduced...

Smooth metric measure spaces, quasi-Einstein metrics, and tractors

Jeffrey Case (2012)

Open Mathematics

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We introduce the tractor formalism from conformal geometry to the study of smooth metric measure spaces. In particular, this gives rise to a correspondence between quasi-Einstein metrics and parallel sections of certain tractor bundles. We use this formulation to give a sharp upper bound on the dimension of the vector space of quasi-Einstein metrics, providing a different perspective on some recent results of He, Petersen and Wylie.

Monopole metrics and the orbifold Yamabe problem

Jeff A. Viaclovsky (2010)

Annales de l’institut Fourier

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We consider the self-dual conformal classes on n # ℂℙ 2 discovered by LeBrun. These depend upon a choice of n points in hyperbolic 3 -space, called monopole points. We investigate the limiting behavior of various constant scalar curvature metrics in these conformal classes as the points approach each other, or as the points tend to the boundary of hyperbolic space. There is a close connection to the orbifold Yamabe problem, which we show is not always solvable (in contrast to the case of compact...