Results 1 to 10 of about 1,044 (116)
On LCK solvmanifolds with a property of Vaisman solvmanifolds
Complex Manifolds, 2022 The purpose in this paper is to determine a locally conformal Kähler solvmanifold such that the nilradical of the solvable Lie group is constructed by a Heisenberg Lie group.
Sawai Hiroshi
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Einstein solvmanifolds are standard [PDF]
Annals of Mathematics, 2007 We study Einstein manifolds admitting a transitive solvable Lie group of isometries (solvmanifolds). It is conjectured that these exhaust the class of noncompact homogeneous Einstein manifolds. J. Heber has showed that under certain simple algebraic condition called standard (i.e.
Jorge Lauret
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New supersymmetric vacua on solvmanifolds [PDF]
Journal of High Energy Physics, 2016 We obtain new supersymmetric flux vacua of type II supergravities on four-dimensional Minkowski times six-dimensional solvmanifolds. The orientifold O4, O5, O6, O7, or O8-planes and D-branes are localized. All vacua are in addition not T-dual to a vacuum
Andriot, David
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Flat Bundles and Hyper-Hodge Decomposition on Solvmanifolds [PDF]
, 2014 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
Hisashi Kasuya
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Vaisman metrics on solvmanifolds and Oeljeklaus-Toma manifolds [PDF]
, 2012 We prove the non-existence of Vaisman metrics on some solvmanifolds with left-invariant complex structures. By this theorem, we show that Oeljeklaus-Toma manifolds does not admit Vaisman metrics.Comment: 12 page.
Hisashi Kasuya
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Cohomologically symplectic solvmanifolds are symplectic [PDF]
Journal of Symplectic Geometry, 2011 We consider aspherical manifolds with torsion-free virtually polycyclic fundamental groups, constructed by Baues. We prove that if those manifolds are cohomologically symplectic then they are symplectic. As a corollary we show that cohomologically symplectic solvmanifolds are symplectic.
Hisashi Kasuya
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Locally conformally Kähler solvmanifolds: a survey [PDF]
Complex Manifolds, 2019 A Hermitian structure on a manifold is called locally conformally Kähler (LCK) if it locally admits a conformal change which is Kähler. In this survey we review recent results of invariant LCK structures on solvmanifolds and present original results ...
Andrada A., Origlia M.
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Pseudo-Riemannian Sasaki solvmanifolds [PDF]
, 2022 We study a class of left-invariant pseudo-Riemannian Sasaki metrics on solvable Lie groups, which can be characterized by the property that the zero level set of the moment map relative to the action of some one-parameter subgroup $\{\exp tX\}$ is a normal nilpotent subgroup commuting with $\{\exp tX\}$, and $X$ is not lightlike.
Diego Conti +2 more
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The Anosov theorem for exponential solvmanifolds [PDF]
Pacific Journal of Mathematics, 1995 A well-known lower bound for the number of fixed points of a self-map / : X -> X is the Nielsen number N(f). Unfortunately, the Nielsen number is difficult to calculate. The Lefschetz number £(/), on the other hand, is readily computable, but usually does not estimate the number of fixed points.
Edward C. Keppelmann, Christopher McCord
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Lattices, cohomology and models of six dimensional almost abelian solvmanifolds
, 2012 We construct lattices on six dimensional not completely solvable almost abelian Lie groups, for which the Mostow condition does not hold. For the corresponding compact quotients, we compute the de Rham cohomology (which does not agree in general with the
Sergio Console, Maura Macrì
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