Displaying similar documents to “On metrics of positive Ricci curvature conformal to M × 𝐑 m ”

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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Volume and area renormalizations for conformally compact Einstein metrics

Graham, Robin C.

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Let X be the interior of a compact manifold X ¯ of dimension n + 1 with boundary M = ∂ X , and g + be a conformally compact metric on X , namely g ¯ ≡ r 2 g + extends continuously (or with some degree of smoothness) as a metric to X , where r denotes a defining function for M , i.e. r > 0 on X and r = 0 , d r ≠ 0 on M . The restrction of g ¯ to T M rescales upon changing r , so defines invariantly a conformal class of metrics on M , which is called the conformal infinity of g + . In the present paper, the author considers conformally compact...

Conformal gradient vector fields on a compact Riemannian manifold

Sharief Deshmukh, Falleh Al-Solamy (2008)

Colloquium Mathematicae

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It is proved that if an n-dimensional compact connected Riemannian manifold (M,g) with Ricci curvature Ric satisfying 0 < Ric ≤ (n-1)(2-nc/λ₁)c for a constant c admits a nonzero conformal gradient vector field, then it is isometric to Sⁿ(c), where λ₁ is the first nonzero eigenvalue of the Laplacian operator on M. Also, it is observed that existence of a nonzero conformal gradient vector field on an n-dimensional compact connected Einstein manifold...