Results 51 to 60 of about 65 (63)
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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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VAISMAN STRUCTURES ON LCK SOLVMANIFOLDS
Tsukuba Journal of Mathematics, 2023An 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, 1985Translation 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, 1988A 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, 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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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 complex solvmanifolds and affine structures
Annali di Matematica Pura ed Applicata, 1985There 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, 2001The 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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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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