Parabolic geometries as conformal infinities of Einstein metrics
Olivier Biquard, Rafe Mazzeo (2006)
Archivum Mathematicum
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Olivier Biquard, Rafe Mazzeo (2006)
Archivum Mathematicum
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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.
Chang, Sun-Yung A., Qing, Jie, Yang, Paul (2007)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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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.
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...