Results 131 to 140 of about 1,529 (146)

INFRA-SOLVMANIFOLDS OF TYPE (R)

The Quarterly Journal of Mathematics, 1995
Für eine einfach zusammenhängende auflösbare Liesche Gruppe \(G\) wird das semidirekte Produkt \(\text{Aff} (G):=\Aut (G) \ltimes G\) als affine Gruppe von \(G\) bezeichnet. Ist nun \(\Gamma\) ein cokompaktes Gitter in \(G\) und \(\pi\leq\text{Aff}(G)\) eine torsionsfreie endliche Erweiterung von \(\Gamma\), \(\Gamma \vartriangleleft \pi\), so nennt ...
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A note on compact solvmanifolds with Kahler structures

, 2004
In this note we show that a compact solvmanifold admits a Kstructure if and only if it is a finite quotient of a complex torus which has a structure of a com- plex torus bundle over a complex torus.
K. Hasegawa
semanticscholar   +1 more source

On complex solvmanifolds and affine structures

Annali di Matematica Pura ed Applicata, 1985
There is a conjecture of \textit{A. Silva} [Rend. Semin. Mat., Torino 1983, Special Issue, 172-192 (1984)] that for the class of compact complex manifolds being affine is equivalent to being a solvmanifold. In this paper the authors show the existence of affine structures on solvmanifolds which satisfy their so-called K-condition.
Andreatta, Marco, L. Alessandrini
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Standard Einstein Solvmanifolds as Critical Points

The Quarterly Journal of Mathematics, 2001
The paper characterizes the rank-one Einstein solvmanifolds of a given dimension as the critical points of the modified scalar curvature functional. Let \((\mathfrak n, \langle\cdot,\cdot\rangle)\) be a fixed \(n\)-dimensional inner product space. Each element \(\mu\in \Lambda^2{\mathfrak n}^\ast\otimes{\mathfrak n}\) can be viewed as a bilinear skew ...
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Determining the translational part of the fundamental group of an infra-solvmanifold of type (R)

Mathematical Proceedings of the Cambridge Philosophical Society, 1997
K. Dekimpe
semanticscholar   +1 more source

A Pseudo-Kähler Structure on a Nontoral Compact Complex Parallelizable Solvmanifold

, 2005
Takumi Yamada
semanticscholar   +1 more source

Curvatures on Vaisman solvmanifolds

Kodai Mathematical Journal
A locally conformal Kähler manifold \((M^{2n}, g, J)\) is called a Vaisman manifold if its Lee form is parallel with respect to the Levi-Civita connection \(\nabla \) of the metric \(g\). Denote \(H\) the \((2n+1)\)-dimensional Heisenberg Lie group and \(\Gamma \) a lattice in \(H\). A Kodaira-Thurston manifold is a nilmanifold \(S^1 \times \Gamma /H\).
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A non-Vaisman LCK solvmanifold associated to a one-dimensional extension of a 2-step nilmanifold

Differential geometry and its applications
Hiroshi Sawai
semanticscholar   +1 more source

Solvmanifolds

1997
Aleksy Tralle, John Oprea
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Presentations of Solvmanifolds

American Journal of Mathematics, 1972
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