Displaying similar documents to “A new variational characterization of compact conformally flat 4-manifolds”

Almost-Einstein manifolds with nonnegative isotropic curvature

Harish Seshadri (2010)

Annales de l’institut Fourier

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Let ( M , g ) , n ≥ 4 , be a compact simply-connected Riemannian n -manifold with nonnegative isotropic curvature. Given 0 < l ≤ L , we prove that there exists ε = ε ( l , L , n ) satisfying the following: If the scalar curvature s of g satisfies l ≤ s ≤ L and the Einstein tensor satisfies Ric - s n g ≤ ε then M is diffeomorphic to a symmetric space of compact type. This is related to the result of S. Brendle on the metric rigidity of Einstein manifolds with nonnegative isotropic curvature. ...

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.

On Affine Connections in a Riemannian Manifold with a Circulant Metric and two Circulant Affinor Structures Върху афинни свързаности в риманово многообразие с циркулантна метрика и две циркулантни афинорни структури

Dokuzova, Iva, Razpopov, Dimitar (2011)

Union of Bulgarian Mathematicians

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Ива Р. Докузова, Димитър Р. Разпопов - В настоящата статия е разгледан клас V оттримерни риманови многообразия M с метрика g и два афинорни тензора q и S. Дефинирана е и друга метрика ¯g в M. Локалните координати на всички тези тензори са циркулантни матрици. Намерени са: 1) зависимост между тензора на кривина R породен от g и тензора на кривина ¯R породен от ¯g; 2) тъждество за тензора на кривина R в случая, когато тензорът на кривина ¯R се анулира; 3) зависимост между секционната кривина...

On Uniqueness Theoremsfor Ricci Tensor

Marina B. Khripunova, Sergey E. Stepanov, Irina I. Tsyganok, Josef Mikeš (2016)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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In Riemannian geometry the prescribed Ricci curvature problem is as follows: given a smooth manifold M and a symmetric 2-tensor r , construct a metric on M whose Ricci tensor equals r . In particular, DeTurck and Koiso proved the following celebrated result: the Ricci curvature uniquely determines the Levi-Civita connection on any compact Einstein manifold with non-negative section curvature. In the present paper we generalize the result of DeTurck and Koiso for a Riemannian manifold with...