Results 41 to 50 of about 1,044 (116)
Cohomologically Kähler manifolds with no Kähler metrics
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 52, Page 3315-3325, 2003., 2003 We show some examples of compact symplectic solvmanifolds, of dimension greater than four, which are cohomologically Kähler and do not admit Kähler metric since their fundamental groups cannot be the fundamental group of any compact Kähler manifold. Some of the examples that we study were considered by Benson and Gordon (1990).
Marisa Fernández +2 more
wiley +1 more source
Kahler Structures on Compact Solvmanifolds [PDF]
Proceedings of the American Mathematical Society, 1990 In a previous paper, the authors proved that the only compact nilmanifolds Γ ∖ G \Gamma \backslash G which admit Kähler structures are tori. Here we consider a more general class of homogeneous spaces Γ ∖ G \Gamma \backslash G , where G G is a ...
Carolyn S. Gordon, Chal Benson
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Central theorems for cohomologies of certain solvable groups [PDF]
, 2015 We show that the group cohomology of torsion-free virtually polycyclic groups and the continuous cohomology of simply connected solvable Lie groups can be computed by the rational cohomology of algebraic groups. Our results are generalizations of certian
Kasuya, Hisashi
core +1 more source
$G_2$-structures on Einstein solvmanifolds [PDF]
Asian Journal of Mathematics, 2015 We study the $G_2$ analogue of the Goldberg conjecture on non-compact solvmanifolds. In contrast to the almost-K hler case we prove that a 7-dimensional solvmanifold cannot admit any left-invariant calibrated $G_2$-structure $ $ such that the induced metric $g_ $ is Einstein, unless $g_ $ is flat.
M. Fernandez +2 more
openaire +3 more sources
Complex structures of splitting type [PDF]
, 2016 We study the six-dimensional solvmanifolds that admit complex structures of splitting type classifying the underlying solvable Lie algebras. In particular, many complex structures of this type exist on the Nakamura manifold $X$, and they allow us to ...
Angella, Daniele +3 more
core +3 more sources
On Ricci negative solvmanifolds and their nilradicals [PDF]
Mathematische Nachrichten, 2019 AbstractIn the homogeneous case, the only curvature behavior which is still far from being understood is Ricci negative. In this paper, we study which nilpotent Lie algebras admit a Ricci negative solvable extension. Different unexpected behaviors were found. On the other hand, given a nilpotent Lie algebra, we consider the space of all the derivations
Deré, Jonas, Lauret, Jorge Ruben
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Ricci Nilsoliton Black Holes [PDF]
, 2008 We follow a constructive approach and find higher-dimensional black holes with Ricci nilsoliton horizons. The spacetimes are solutions to Einstein's equation with a negative cosmological constant and generalises therefore, anti-de Sitter black hole ...
Aebischer +35 more
core +5 more sources
Ricci soliton solvmanifolds [PDF]
Journal für die reine und angewandte Mathematik (Crelles Journal), 2011 18 pages, to appear in Crelle's ...
openaire +3 more sources
Formality and hard Lefschetz property of aspherical manifolds [PDF]
, 2012 For a Lie group $G=\R^{n}\ltimes_{\phi}\R^{m}$ with the semi-simple action $\phi:\R^{n}\to {\rm Aut}(\R^{m})$, we show that if $\Gamma$ is a finite extension of a lattice of $G$ then $K(\Gamma, 1)$ is formal.
Kasuya, Hisashi
core +3 more sources
Einstein solvmanifolds: existence and non-existence questions
, 2010 The general aim of this paper is to study which are the solvable Lie groups admitting an Einstein left invariant metric. The space N of all nilpotent Lie brackets on R^n parametrizes a set of (n+1)-dimensional rank-one solvmanifolds, containing the set ...
Lauret, Jorge, Will, Cynthia
core +1 more source