Results 51 to 60 of about 444 (112)

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 line bundles arising from the LCK structure over locally conformal Kähler solvmanifolds

Complex Manifolds
We can construct a real line bundle arising from the locally conformal Kähler (LCK) structure over an LCK manifold. We study the properties of this line bundle over an LCK solvmanifold whose complex structure is left-invariant. Mainly, we prove that this
Yamada Takumi
doaj   +1 more source

Maximal symmetry and unimodular solvmanifolds [PDF]

Pacific Journal of Mathematics, 2019
Recently, it was shown that Einstein solvmanifolds have maximal symmetry in the sense that their isometry groups contain the isometry groups of any other left-invariant metric on the given Lie group. Such a solvable Lie group is necessarily non-unimodular.
openaire   +3 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

Function theory on metabelian solvmanifold

Journal of Functional Analysis, 1972
AbstractThe Laplace operators for metabelian solvmanifolds are used to describe certain spaces of C∞ functions on metabelian solvmanifolds of interest in harmonic analysis.
openaire   +2 more sources

On the d-invariant of compact solvmanifolds.

Journal für die reine und angewandte Mathematik (Crelles Journal), 1985
Let G be a connected real Lie group and \(\Gamma\) a closed subgroup of G. Then \(\Gamma\) is called a lattice if G/\(\Gamma\) is compact. Every basis of the Lie algebra \({\mathfrak g}\) of G determines a parallelization of G/\(\Gamma\) and hence by the Thom-Pontryagin construction an element [G/\(\Gamma\) ], the stable homotopy of spheres. Earlier by
Singhof, W., Deninger, Ch.
openaire   +1 more source

Homogeneous Einstein metrics on Euclidean spaces are Einstein solvmanifolds [PDF]

, 2018
We show that homogeneous Einstein metrics on Euclidean spaces are Einstein solvmanifolds, using that they admit periodic, integrally minimal foliations by homogeneous hypersurfaces.
Böhm, Christoph, Lafuente, Ramiro A.
core   +1 more source

LOCALLY CONFORMAL KÄHLER STRUCTURES ON COMPACT SOLVMANIFOLDS [PDF]

Let (M,g,J) be a compact Hermitian manifold and Ω the fundamental 2-form of (g,J). A Hermitian manifold (M,g,J) is said to be locally conformal Kähler if there exists a closed 1-form ω such that dΩ=ω∧Ω.
Sawai, Hiroshi
core   +2 more sources

Einstein solvmanifolds are standard [PDF]

Annals of Mathematics, 2010
We study Einstein manifolds admitting a transitive solvable Lie group of isometries (solvmanifolds). It is conjectured that these exhaust the class of noncompact homogeneous Einstein manifolds. J. Heber has showed that under certain simple algebraic condition called standard (i.e.
openaire   +2 more sources

Small deformations and non-left-invariant complex structures on six-dimensional compact solvmanifolds [PDF]

, 2010
We observed in our previous paper that all the complex structures on four-dimensional compact solvmanifolds, including tori, are left-invariant. In this paper we will give an example of a six-dimensional compact solvmanifold which admits a continuous ...
Hasegawa, Keizo
core   +1 more source