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Einstein Manifolds As Yang-Mills Instantons [PDF]
Modern Physics Letters A, 2013 It is well-known that Einstein gravity can be formulated as a gauge theory of Lorentz group where spin connections play a role of gauge fields and Riemann curvature tensors correspond to their field strengths.
Donaldson S. K. +6 more
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Anatomy of Einstein manifolds [PDF]
Physical Review D, 2022 v2: Title changed with improved contents, 36 pages, 4 figures, to appear in Phys.
Jongmin Park +2 more
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On a semi-quasi-Einstein manifold [PDF]
Journal of Geometry and Physics, 2020 In the present paper we introduce a semi-quasi-Einstein manifold from a semi symmetric metric connection. Among others, the popular Schwarzschild and Kottler spacetimes are shown to possess this structure. Certain curvature conditions are studied in such a manifold with a Killing generator.
Yanling Han, Avik De, Peibiao Zhao
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On conformally Kähler, Einstein manifolds [PDF]
Journal of the American Mathematical Society, 2008 We prove that any compact complex surface with c 1 > 0 c_1>0 admits an Einstein metric which is conformally related to a Kähler metric. The key new ingredient is the existence of such a metric on the blow-up C P 2
Chen, Xiuxiong +2 more
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On Einstein Equations on Manifolds and Supermanifolds [PDF]
Journal of Nonlinear Mathematical Physics, 2002 The Einstein equations (EE) are certain conditions on the Riemann tensor on the real Minkowski space M. In the twistor picture, after complexification and compactification M becomes the Grassmannian $Gr_{2}^{4}$ of 2-dimensional subspaces in the 4-dimensional complex one.
Leites, D., Poletaeva, E., Serganova, V.
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Examples of Einstein manifolds in odd dimensions [PDF]
, 2011 We construct Einstein metrics of non-positive scalar curvature on certain solid torus bundles over a Fano Kahler-Einstein manifold. We show, among other things, that the negative Einstein metrics are conformally compact, and the Ricci-flat metrics have ...
Chen, Dezhong
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Sasaki-Einstein manifolds [PDF]
Surveys in Differential Geometry, 2011 This article is an overview of some of the remarkable progress that has been made in Sasaki-Einstein geometry over the last decade, which includes a number of new methods of constructing Sasaki-Einstein manifolds and obstructions.
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Einstein manifolds and contact geometry [PDF]
Proceedings of the American Mathematical Society, 2001 We show that every K-contact Einstein manifold is Sasakian-Einstein and discuss several corollaries of this result.
Boyer, Charles P., Galicki, Krzysztof
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REMARKS ON KÄHLER-EINSTEIN MANIFOLDS [PDF]
Nagoya Mathematical Journal, 1972 The main purpose of this note is to characterize a compact Káhler-Einstein manifold in terms of curvature form. The curvature form Q is an EndT valued differential form of type (1,1) which represents the curvature class of the manifold. We shall prove that the curvature form of a Káhler metric is the harmonic representative of the curvature class if ...
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EINSTEIN MANIFOLDS WITH SKEW TORSION [PDF]
The Quarterly Journal of Mathematics, 2013 24 pages, 1 figure, new version with erratum added at the ...
Ferreira, Ana Cristina, Agricola, Ilka
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