Results 91 to 100 of about 163 (116)

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 \(S^1 \times \Gamma /H\).
Hiroshi Sawai
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Fixed points on model solvmanifold pairs [PDF]

Journal of Pure and Applied Algebra, 2008
In this paper we define model solvmanifold pairs and their diagonal type selfmaps in the tradition of Heath and Keppelmann. We derive an explicit formula for computing the relative Nielsen number N(F;X,A) on these spaces and selfmaps F:(X,A)→(X,A).
Reite, Aaron
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Three-step Harmonic Solvmanifolds

Geometriae Dedicata, 2003
The authors define a solvmanifold as a connected and simply connected solvable Lie group together with a left-invariant metric. Damek-Ricci spaces are examples of solvmanifolds. These spaces appeared as counter-examples for the Lichnerowicz conjecture, namely, that every harmonic Riemannian manifold would be locally isometric to a two-point homogeneous
Benson, Chal, Payne, Tracy L., Ratcliff, Gail   +2 more
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FLOWS ON COMPACT SOLVMANIFOLDS

Mathematics of the USSR-Sbornik, 1985
Translation from Mat. Sb., Nov. Ser. 123(165), No.4, 549-558 (Russian) (1984; Zbl 0545.28013).
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Characteristic Classes of Compact Solvmanifolds

The Annals of Mathematics, 1962
A solvmanifold (nilmanifold) is the homogeneous space of a connected solvable (nilpotent) Lie group. A theorem of A. I. Malcev [3] states that a nilmanifold can always be expressed as the quotient of a nilpotent Lie group by a discrete subgroup. From this it follows easily that nilmanifolds are parallelizable.
Auslander, Louis, Szczarba, R. H.
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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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On Formality and Solvmanifolds [PDF]

, 2008
Topology of symplectic manifolds is nowadays a subject of intensive development. The simplest examples of such manifolds are Kähler manifolds and an important property of the latter is their formality. Thus, a possible way of constructing symplectic manifolds with no Kähler structure is to find such ones which are not formal. M. Fernández und V.
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Model solvmanifolds for Lefschetz and Nielsen theories

Quaestiones Mathematicae, 2002
In this paper we construct a class of solvmanifolds and certain (diagonal type) self maps on them. These solvmanifolds and their maps serve firstly as rich source of examples. Secondly they serve as models for Nielsen theory in the sense that any map f : S → S of an arbitrary compact solvmanifold S, has the same Lefschetz and Nielsen theory ...
Heath, Philip R, Keppelmann, Edward C
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Presentations of Solvmanifolds

American Journal of Mathematics, 1972
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Splitting Theorems and the Structure of Solvmanifolds

The Annals of Mathematics, 1970
Auslander, Louis, Tolimieri, Richard
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