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Generalized Einstein manifolds
Journal of Geometry and Physics, 1995The geometrization of physics, especially regarding the equations of electromagnetism and gravitation in general relativity, has been a vital problem of investigation for a long time. A. Einstein himself devoted the last several years of his life to realize this dream without success. However, taking grant of two axioms proposed by \textit{D. Hilbert} [
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Journal of Geometry and Physics, 2004
Topological obstructions to the existence of Einstein metrics on a given compact and oriented 4-manifold were found by \textit{N. Hitchin} [J. Differ. Geom. 9, 435--441 (1974; Zbl 0281.53039)] and by \textit{M. J. Gursky} and \textit{C. LeBrun} [Ann. Global Anal. Geom. 17, No. 4, 315--328 (1999; Zbl 0967.53029)].
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Topological obstructions to the existence of Einstein metrics on a given compact and oriented 4-manifold were found by \textit{N. Hitchin} [J. Differ. Geom. 9, 435--441 (1974; Zbl 0281.53039)] and by \textit{M. J. Gursky} and \textit{C. LeBrun} [Ann. Global Anal. Geom. 17, No. 4, 315--328 (1999; Zbl 0967.53029)].
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On Einstein Hermitian manifolds [PDF]
Monatshefte für Mathematik, 2007 We show that every compact Einstein Hermitian surface with constant *–scalar curvature is a Kahler surface. In contrast to the 4-dimensional case, it is shown that there exists a compact Einstein Hermitian (4n + 2)-dimensional manifold with constant *–scalar curvature which is not Kahler.
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Spin Holonomy of Einstein Manifolds
Communications in Mathematical Physics, 1999zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On Strongly Inhomogeneous Einstein Manifolds
Bulletin of the London Mathematical Society, 1996The present authors constructed in [J. Reine Angew. Math. 455, 183-220 (1994)] inhomogeneous Einstein metrics of positive scalar curvature on compact simply connected 3-Sasakian manifolds \((S(p),g(p))\) in dimension \(4n-5\) for all \(n\geq 3\).
Benjamin M. Mann +2 more
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2018
A Kahler manifold (M, g) is Einstein when there exists \(\lambda \in \mathbb {R}\) such that ρ = λω, where ω is the Kahler form associated to g and ρ is its Ricci form. The constant λ is called the Einstein constant and it turns out that λ = s∕2n, where s is the scalar curvature of the metric g and n the complex dimension of M (as a general reference ...
Michela Zedda, Andrea Loi
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A Kahler manifold (M, g) is Einstein when there exists \(\lambda \in \mathbb {R}\) such that ρ = λω, where ω is the Kahler form associated to g and ρ is its Ricci form. The constant λ is called the Einstein constant and it turns out that λ = s∕2n, where s is the scalar curvature of the metric g and n the complex dimension of M (as a general reference ...
Michela Zedda, Andrea Loi
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Rigidity of Einstein manifolds and generalized quasi-Einstein manifolds
Annales Polonici Mathematici, 2015Li Ping Luo, Yi Hua Deng, Li Jun Zhou
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The Extension of Einstein Manifolds
1981Of the many mathematical problems connected with general relativity, the extension problem has been chosen for discussion in this chapter, because it is concerned with the global geometrical and topological properties of Einstein manifolds, and those properties seem to me to constitute the most basically mathematical aspect of the theory.
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Einstein Manifolds and Topology
1987Which compact manifolds do admit an Einstein metric? Except in dimension 2 (see Section B of this chapter), a complete answer to this question seems out of reach today. At least, in dimensions 3 and 4, we can single out a few manifolds which definitely do not admit any Einstein metric.
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