Results 71 to 80 of about 1,208 (130)
SYZ mirror symmetry of solvmanifolds
Annali di Matematica Pura ed Applicata (1923 -)AbstractWe present an effective construction of non-Kähler supersymmetric mirror pairs in the sense of Lau, Tseng and Yau (Commun. Math. Phys. 340:145–170, 2015) starting from left-invariant affine structures on Lie groups. Applying this construction we explicitly find SYZ mirror symmetric partners of all known compact 6-dimensional completely solvable
Bedulli, Lucio, Vannini, Alessandro
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Compact CR-solvmanifolds as Kähler obstructions [PDF]
Mathematische Zeitschrift, 2010 We give a precise characterization for when a compact CR-solvmanifold is CR-embeddable in a complex Kahler manifold. Equivalently this gives a non-Kahler criterion for complex manifolds containing CR-solvmanifolds not satisfying these conditions. This paper is the natural continuation of Oeljeklaus and Richthofer [J Differ Geom 27(3):399–421, 1988] and
Gilligan, Bruce, Oeljeklaus, Karl
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Formality and symplectic structures of almost abelian solvmanifolds [PDF]
arXiv, 2013 In this paper we study some properties of almost abelian solvmanifolds using minimal models associated to a fibration. In particular we state a necessary and sufficient condition to formality and a method for finding symplectic strucures of this kind of solvmanifolds.
arxiv
arXiv, 2003 Compact K\"ahler solvmanifolds are classified up to biholomorphism. A proof of a conjecture Benson and Gordon, that completely solvable compact K\"ahler solvmanifolds are tori is deduced from this. The main ingredient in the proof is a restriction theorem for polycyclic K\"ahler groups proved by Nori and the author.
arxiv
A note on compact solvmanifolds with Kaehler structures [PDF]
Osaka Journal of Mathematics, 2004 A solvmanifold is a compact differentiable manifold M on which a connected solvable Lie group G acts transitively. As the main result, we will see, applying a result of Arapura and Nori on solvable Kaehler groups and some of the author's previous results, that a compact solvmanifold admits a Kaehler structure if and only if it is a finite quotient of a
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Noncompact homogeneous Einstein manifolds attached to graded Lie algebras [PDF]
arXiv, 2006 In this paper, we study the nilradicals of parabolic subalgebras of semisimple Lie algebras and the natural one-dimensional solvable extensions of them. We investigate the structures, curvatures and Einstein conditions of the associated nilmanifolds and solvmanifolds. We show that our solvmanifold is Einstein if the nilradical is of two-step.
arxiv
Isometry groups of Riemannian solvmanifolds
Transactions of the American Mathematical Society, 1988 A simply connected solvable Lie group R R together with a left-invariant Riemannian metric g g is called a (simply connected) Riemannian solvmanifold. Two Riemannian solvmanifolds ( R , g ) (R,\,g) and ( R ′
Carolyn S. Gordon, Edward N. Wilson
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On the equivalence of several definitions of compact infra-solvmanifolds [PDF]
Proc. Japan Acad. Ser. A Math. Sci. 89 (2013), no. 9, 114-118, 2013 We show the equivalence of several definitions of compact infra-solvmanifolds that appear in various math literatures.
arxiv
The Ricci flow in a class of solvmanifolds
Differential Geometry and its Applications, 2013 16 pages, 1 ...
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Flat bundles and Hyper-Hodge decomposition on solvmanifolds [PDF]
arXiv, 2013 We study rank $1$ flat bundles over solvmanifolds whose cohomologies are non-trivial. By using Hodge theoretical properties for all topologically trivial rank $1$ flat bundles, we represent the structure theorem of K\"ahler solvmanifolds as extensions of Hasegawa's result and Benson-Gordon's result for nilmanifolds.
arxiv