Search Results - "LeBrun, Claude"
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The Einstein–Maxwell equations, Kähler metrics, and Hermitian geometry
Published in Journal of geometry and physics (01-05-2015)“…Any constant-scalar-curvature Kähler (cscK) metric on a complex surface may be viewed as a solution of the Einstein–Maxwell equations, and this allows one…”
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The Einstein–Maxwell Equations and Conformally Kähler Geometry
Published in Communications in mathematical physics (01-06-2016)Get full text
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On Conformally Kähler, Einstein Manifolds
Published in Journal of the American Mathematical Society (01-10-2008)“…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…”
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A Multisite Campaign to Measure Solar-like Oscillations in Procyon. I. Observations, Data Reduction, and Slow Variations
Published in The Astrophysical journal (10-11-2008)“…We have carried out a multisite campaign to measure oscillations in the F5 star Procyon A. We obtained high-precision velocity observations over more than…”
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Ricci curvature, minimal volumes, and Seiberg-Witten theory
Published in Inventiones mathematicae (01-08-2001)Get full text
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The Einstein–Maxwell Equations and Conformally Kähler Geometry
Published in Communications in mathematical physics (01-06-2016)“…Page’s Einstein metric on CP 2 # CP ¯ 2 is conformally related to an extremal Kähler metric. Here we construct a family of conformally Kähler solutions of the…”
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Yamabe Invariants, Homogeneous Spaces, and Rational Complex Surfaces
Published in Symmetry, integrability and geometry, methods and applications (01-01-2023)“…The Yamabe invariant is a diffeomorphism invariant of smooth compact manifolds that arises from the normalized Einstein-Hilbert functional. This article…”
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Twistors, Self-Duality, and Spinc Structures
Published in Symmetry, integrability and geometry, methods and applications (19-11-2021)“…The fact that every compact oriented 4-manifold admits spinc structures was proved long ago by Hirzebruch and Hopf. However, the usual proof is neither direct…”
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Bach-Flat Kähler Surfaces
Published in The Journal of geometric analysis (01-07-2020)“…A Riemannian metric on a compact 4-manifold is said to be Bach-flat if it is a critical point for the L 2 -norm of the Weyl curvature. When the Riemannian…”
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Mass, Kähler manifolds, and symplectic geometry
Published in Annals of global analysis and geometry (01-07-2019)“…In the author’s previous joint work with Hein (Commun Math Phys 347:183–221, 2016 ), a mass formula for asymptotically locally Euclidean Kähler manifolds was…”
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Einstein metrics, conformal curvature, and anti-holomorphic involutions
Published in Annales mathématiques du Québec (01-10-2021)“…Building on previous results [ 17 , 35 ], we complete the classification of compact oriented Einstein 4-manifolds with det ( W + ) > 0 . There are, up to…”
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Einstein Metrics, Symplectic Minimality, and Pseudo-Holomorphic Curves
Published in Annals of global analysis and geometry (01-09-2005)“…Let (M4, g, omega) be a compact, almost-Kahler-Einstein manifold of negative star-scalar curvature. Then (M, omega) is a minimal symplectic 4-manifold of…”
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Einstein metrics, harmonic forms, and symplectic four-manifolds
Published in Annals of global analysis and geometry (01-06-2015)“…If M is the underlying smooth oriented four-manifold of a Del Pezzo surface, we consider the set of Riemannian metrics h on M such that W + ( ω , ω ) > 0 ,…”
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Gravitational Instantons, Weyl Curvature, and Conformally Kähler Geometry
Published in International mathematics research notices (20-09-2024)“…Abstract In a previous paper [7], the first two authors classified complete Ricci-flat ALF Riemannian 4-manifolds that are toric and Hermitian, but non-Kähler…”
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Counter-examples to the generalized positive action conjecture
Published in Communications in mathematical physics (01-12-1988)Get full text
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Weyl Curvature, Del Pezzo Surfaces, and Almost-Kähler Geometry
Published in The Journal of geometric analysis (01-07-2015)“…If a smooth compact 4 -manifold M admits a Kähler–Einstein metric g of positive scalar curvature, Gursky (Ann Math 148:315–337, 1998 ) showed that its…”
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Mass in Kähler Geometry
Published in Communications in mathematical physics (01-10-2016)“…We prove a simple, explicit formula for the mass of any asymptotically locally Euclidean (ALE) Kähler manifold, assuming only the sort of weak fall-off…”
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Twistors, Kahler Manifolds, and Bimeromorphic Geometry. I
Published in Journal of the American Mathematical Society (01-04-1992)“…By considering deformations of the Moishezon twistor spaces of CP2 #⋯ #CP2 constructed in [20], we show that the blow up of C2 at n points in general position…”
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Yamabe Invariants, Homogeneous Spaces, and Rational Complex Surfaces
Published 07-05-2023“…SIGMA 19 (2023), 027, 11 pages The Yamabe invariant is a diffeomorphism invariant of smooth compact manifolds that arises from the normalized Einstein-Hilbert…”
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Curvature in the Balance: The Weyl Functional and Scalar Curvature of 4-Manifolds
Published 04-03-2022“…The infimum of the Weyl functional is shown to be surprisingly small on many compact 4-manifolds that admit positive-scalar-curvature metrics. Results are also…”
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