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Sasaki-Einstein Manifolds [PDF]
Surveys in Differential Geometry, 2010 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.Comment: 58 pages ...
Sparks, James
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Einstein almost cok\"ahler manifolds
, 2016 We study an odd-dimensional analogue of the Goldberg conjecture for compact Einstein almost K\"ahler manifolds. We give an explicit non-compact example of an Einstein almost cok\"ahler manifold that is not cok\"ahler.
Conti, Diego, Fernández, Marisa
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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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On Sasaki-Einstein manifolds in dimension five
Geometriae Dedicata, 2009 We prove the existence of Sasaki-Einstein metrics on certain simply connected 5-manifolds where until now existence was unknown. All of these manifolds have non-trivial torsion classes.
Charles P Boyer, Michael Nakamaye
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Communications of the Korean Mathematical Society, 2008 The object of the present paper is to study some properties of a quasi Einstein manifold. A non-trivial concrete example of a quasi Einstein manifold is also given.
Uday Chand De
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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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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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