Results 111 to 120 of about 1,005 (125)

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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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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VAISMAN STRUCTURES ON LCK SOLVMANIFOLDS

Tsukuba Journal of Mathematics, 2023
An LCK manifold is a Hermitian manifold \((M,g,J)\) such that the fundamental \(2\)-form \(\Omega\), defined by \(\Omega(X,Y)=g(X,JY)\), satisfies the condition \(d\Omega= \omega\wedge \Omega\) for a closed 1-form \(\omega\). An LCK manifold is said to be Vaisman if \(\omega\) is parallel.
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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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Isometry Groups of Riemannian Solvmanifolds

Transactions of the American Mathematical Society, 1988
A simply connected solvable Lie group R R together with a left-invariant Riemannian metric g g is called a (simply connected) Riemannian solvmanifold. Two Riemannian solvmanifolds ( R , g ) (R,\,g) and ( R ′
Gordon, Carolyn S., Wilson, Edward N.
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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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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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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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Presentations of Solvmanifolds

American Journal of Mathematics, 1972
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