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Three-step Harmonic Solvmanifolds
Geometriae Dedicata, 2003The 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 +2 more
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Characteristic Classes of Compact Solvmanifolds
The Annals of Mathematics, 1962A 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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Lefschetz and Nielsen coincidence numbers on nilmanifolds and solvmanifolds
Topology and Its Applications, 1992 Suppose M1,M2 are compact, connected orientable manifolds of the same dimension. Then for all pairs of maps ƒ,g:M1→M2, the Nielsen coincidence number N(ƒ,g) and the Lefschetz coincidence number L(ƒ,g) are measures of the number of coincidences of ƒ and g:
Christopher K. McCord +1 more
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INFRA-SOLVMANIFOLDS OF TYPE (R)
The Quarterly Journal of Mathematics, 1995Für 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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Curvatures on Vaisman solvmanifolds
Kodai Mathematical JournalA 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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Splitting Theorems and the Structure of Solvmanifolds
The Annals of Mathematics, 1970Auslander, Louis, Tolimieri, Richard
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