Results 51 to 60 of about 146 (116)
, 2003 Compact Kähler solvmanifolds are classified up to biholomorphism. A proof of a conjecture Benson and Gordon, that completely solvable compact Kähler solvmanifolds are tori is deduced from this. The main ingredient in the proof is a restriction theorem for polycyclic Kähler groups proved by Nori and the author.
openaire +2 more sources
Homotopy minimal periods for NR-solvmanifolds maps
, 2004 A natural number m is called the homotopy minimal period of a map f:X→X if every map g homotopic to f will have periodic points of minimal period m. In this paper we give a complete description of the sets of homotopy minimal periods of a map of compact ...
Marzantowicz, Wacław +7 more
core +1 more source
Periodic points on nilmanifolds and solvmanifolds [PDF]
Pacific Journal of Mathematics, 1994 Let \(M\) be a compact manifold and \(f:M \to M\) a self map on \(M\). For any natural number \(n\), the \(n\)-th iterate of \(f\) is the \(n\)-fold composition \(f^ n:M \to M\). The fixed point set of \(f\) is \(\text{fix} (f)=\{x \in M:f(x)=x\}\). We say that \(x \in M\) is a periodic point of \(f\) is \(x\) is a fixed point of some \(f^ n\) and we ...
openaire +3 more sources
Examples of Compact Lefschetz Solvmanifolds
Tokyo Journal of Mathematics, 2002 A symplectic manifold \((M^{2m},\omega)\) is called a Lefschetz manifold if the mapping \(\wedge\omega^{m-1}: H^1_{DR}\to H^{2m-1}_{DR}\) on \(M\) is an isomorphism. By a solvmanifold is meant a homogeneous space \(G/\Gamma\) where \(G\) is a simply connected solvable Lie group and \(\Gamma\) is a lattice.
openaire +2 more sources
On the structure of complex solvmanifolds [PDF]
Journal of Differential Geometry, 1988 A connected complex space X is called a solvmanifold if there is a connected complex solvable Lie group G which acts holomorphically and transitively on it. The aim of the paper is to study two classes of solvmanifolds: i) X is Kähler, ii) X is separable by analytic hypersurfaces.
Oeljeklaus, Karl, Richthofer, Wolfgang
openaire +2 more sources
Compact CR-solvmanifolds as Kähler obstructions.
, 2011 25 pagesInternational audienceWe give a precise characterization for when a compact CR-solvmanifold is CR-embeddable in a complex Kähler manifold. Equivalently this gives a non-Kähler criterion for complex manifolds containing CR-solvmanifolds not ...
Gilligan, Bruce, Oeljeklaus, Karl
core +1 more source
Closed G2-eigenforms and exact G2-structures [PDF]
, 2021 A study is made of left-invariant $\mathrm{G}_2$-structures with an exact 3-form on a Lie group $G$ whose Lie algebra $\mathfrak{g}$ admits a codimension-one nilpotent ideal $\mathfrak{h}$.
Freibert, Marco +1 more
core +1 more source
Solvmanifolds and Generalized Kähler Structures
, 1970 We review generalized complex geometry in relation with solvmanifolds and we describe the construction in [17] of a generalized Kähler structure on a 6-dimensional solvmanifold. The compact manifold is the total space of a 𝕋2-bundle over an Inoue
Tomassini, Adriano, Fino, Anna
core +1 more source
Symplectic harmonicity and generalized coeffective cohomologies [PDF]
, 2019 Relations between the symplectically harmonic cohomology and the coeffective cohomology of a symplectic manifold are obtained. This is achieved through a generalization of the latter, which in addition allows us to provide a coeffective version of the ...
Ugarte, L., Villacampa, R.
core +1 more source
Classification, Cobordism, and Curvature of Four-Dimensional Infra-Solvmanifolds [PDF]
, 2014 Crystallographic groups of solvable Lie groups generalize the crystallographic groups of Euclidean space. The quotient of a solvable Lie group G by the action of a torsion-free crystallographic group of G is an infra-solvmanifold of G.
Thuong, Scott Van
core