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On some euclidean einstein metrics
Letters in Mathematical Physics, 1986The authors study the complex manifold associated with a nonlinear superposition of the Eguchi-Hanson and the pseudo-Fubini-Study metrics. The apparent singularities of the metric can be resolved only if the Eguchi-Hanson parameter satisfies a certain condition with \(n\geq 3\). The authors give a geometrical explanation of this fact.
Pedersen, H., Nielsen, B.
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Mathematische Zeitschrift, 2005
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Einstein metrics and Einstein–Randers metrics on a class of homogeneous manifolds
International Journal of Geometric Methods in Modern Physics, 2018In this paper, we give [Formula: see text]-invariant Einstein metrics on a class of homogeneous manifolds [Formula: see text], and then prove that every homogeneous manifold [Formula: see text] admits at least three families of [Formula: see text]-invariant non-Riemannian Einstein–Randers metrics.
Chao chen, Zhiqi chen, Yuwang Hu
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1998
In this chapter we shall use the continuity method and the method of upper and lower solutions to solve complex Monge—Ampere equations.
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In this chapter we shall use the continuity method and the method of upper and lower solutions to solve complex Monge—Ampere equations.
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Desingularisation of Einstein metrics. I
2013The author studies a new obstruction for a real Einstein 4-orbifold \((M_0,g_0)\) with \(A_1\)-singularity to be a limit of smooth Einstein 4-manifolds. The author proves that if \((M_0,g_0)\) with a nondegenerate asymptotically hyperbolic metric \(g_0\) has a singularity of the type \(\mathbb R^4\slash \mathbb Z_2\) at a point \(p_0\) and \(M\) is a ...
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