Displaying similar documents to “Renormalized volume and the evolution of APEs”

On metrics of positive Ricci curvature conformal to M × 𝐑 m

Juan Miguel Ruiz (2009)

Archivum Mathematicum

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Let ( M n , g ) be a closed Riemannian manifold and g E the Euclidean metric. We show that for m > 1 , M n × 𝐑 m , ( g + g E ) is not conformal to a positive Einstein manifold. Moreover, M n × 𝐑 m , ( g + g E ) is not conformal to a Riemannian manifold of positive Ricci curvature, through a radial, integrable, smooth function, ϕ : 𝐑 𝐦 → 𝐑 + , for m > 1 . 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)

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.

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 4 -manifolds with a conformal vector field and abelian monopoles on Einstein-Weyl 3 -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...