The odd-dimensional Goldberg conjecture
TLDR
In this article, an odd-dimensional version of the Goldberg conjecture was formulated and proved by using an orbifold analogue of Sekigawa's arguments in [8], and an approximation argument of K -contact structures with quasiregular ones.Abstract:
An odd-dimensional version of the Goldberg conjecture was formulated and proved in [5], by using an orbifold analogue of Sekigawa's arguments in [8], and an approximation argument of K -contact structures with quasiregular ones. We provide here another proof of this result. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)read more
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Almost ricci solitons and k-contact geometry
TL;DR: In this article, the authors give a short Lie-derivative theoretic proof of the following recent result of Barros et al. that a compact almost Ricci soliton with constant scalar curvature is gradient, and isometric to a Euclidean sphere.
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A Generalization of the Goldberg Conjecture for CoKähler Manifolds
TL;DR: The Ricci-flat Ricci solitons with the potential vector fields pointwise collinear with the Reeb vector fields on K-almost coKahler manifolds were studied in this article.
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Seiberg-Witten invariants on manifolds with Riemannian foliations of codimension 4
TL;DR: In this article, the Seiberg-Witten equations on closed manifolds endowed with a Riemannian foliation of codimension 4 were defined and the compactness of the moduli space under some hypothesis satisfied for instance by closed K -contact manifolds was shown.
Einstein-like conditions and cosymplectic geometry
TL;DR: In this paper, it was shown that every Einstein compact almost C-manifold M 2n+s whose Reeb vector fields are Killing is a C manifold.
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Quasi-einstein contact metric manifolds
TL;DR: In this paper, the authors consider quasi-Einstein metrics in the framework of contact metric manifolds and prove rigidity results for (κ, μ)-spaces, and show that any complete K-contact manifold with quasi-einstein metric is compact Einstein and Sasakian.
References
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Riemannian Geometry of Contact and Symplectic Manifolds
TL;DR: In this article, the authors describe a complex geometry model of Symplectic Manifolds with principal S1-bundles and Tangent Sphere Bundles, as well as a negative Xi-sectional Curvature.
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On some compact Einstein almost Kähler manifolds
TL;DR: Soit M=(M 4, J, ) une variete d'Einstein compacte presque de Kahler dont la courbure scalaire est non negative as mentioned in this paper.
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Équations différentielles caractéristiques de la sphère
TL;DR: Gauthier-Villars as mentioned in this paper implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/conditions).
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Einstein manifolds and contact geometry
TL;DR: In this article, it was shown that every K-contact Einstein manifold is SasakianEinstein and several corollaries of this result were discussed, e.g., the relation between the two manifold types.