Parabolic geometries as conformal infinities of Einstein metrics
Olivier Biquard, Rafe Mazzeo (2006)
Archivum Mathematicum
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Displaying similar documents to “Renormalized volume and the evolution of APEs”
Parabolic geometries as conformal infinities of Einstein metrics
On metrics of positive Ricci curvature conformal to
Juan Miguel Ruiz (2009)
Archivum Mathematicum
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Let be a closed Riemannian manifold and the Euclidean metric. We show that for , is not conformal to a positive Einstein manifold. Moreover, is not conformal to a Riemannian manifold of positive Ricci curvature, through a radial, integrable, smooth function, , for . These results are motivated by some recent questions on Yamabe constants.
Some progress in conformal geometry.
Chang, Sun-Yung A., Qing, Jie, Yang, Paul (2007)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Smooth metric measure spaces, quasi-Einstein metrics, and tractors
Jeffrey Case (2012)
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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.
Selfdual spaces with complex structures, Einstein-Weyl geometry and geodesics
David M J. Calderbank, Henrik Pedersen (2000)
Annales de l'institut Fourier
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We study the Jones and Tod correspondence between selfdual conformal -manifolds with a conformal vector field and abelian monopoles on Einstein-Weyl -manifolds, and prove that invariant complex structures correspond to shear-free geodesic congruences. Such congruences exist in abundance and so provide a tool for constructing interesting selfdual geometries with symmetry, unifying the theories of scalar-flat Kähler metrics and hypercomplex structures with symmetry. We also show that...