Results 31 to 40 of about 163 (116)

Bott–Chern cohomology of solvmanifolds [PDF]

Annals of Global Analysis and Geometry, 2017
We study conditions under which sub-complexes of a double complex of vector spaces allow to compute the Bott-Chern cohomology. We are especially aimed at studying the Bott-Chern cohomology of special classes of solvmanifolds, namely, complex parallelizable solvmanifolds and solvmanifolds of splitting type.
Angella, Daniele, Kasuya, Hisashi
openaire   +2 more sources

Six dimensional homogeneous spaces with holomorphically trivial canonical bundle [PDF]

, 2023
We classify all the $6$-dimensional unimodular Lie algebras $\mathfrak{g}$ admitting a complex structure with non-zero closed $(3,0)$-form. This gives rise to $6$-dimensional compact homogeneous spaces $M=\Gamma\backslash G$, where $\Gamma$ is a lattice,
Ugarte, L., Otal, A.
core   +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

A Sheaf‐Theoretic CR Reduction for Levi‐Flat Manifolds Beyond the Kähler Setting

International Journal of Mathematics and Mathematical Sciences, Volume 2026, Issue 1, 2026.
This paper develops a sheaf‐theoretic reduction formalism for real‐analytic homogeneous CR manifolds realized as orbits in complex homogeneous manifolds. Let M = G0/H0 be such a CR manifold, let M↪X be a complex realization, and let π : X⟶Y be the holomorphic reduction of the ambient complex manifold.
Abdel Rahman Al-Abdallah, Shikha Binwal
wiley   +1 more source

Solvmanifolds and Generalized Kähler Structures [PDF]

, 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

Twisted conjugacy in soluble arithmetic groups

Mathematische Nachrichten, Volume 298, Issue 3, Page 763-793, March 2025.
Abstract Reidemeister numbers of group automorphisms encode the number of twisted conjugacy classes of groups and might yield information about self‐maps of spaces related to the given objects. Here, we address a question posed by Gonçalves and Wong in the mid‐2000s: we construct an infinite series of compact connected solvmanifolds (that are not ...
Paula M. Lins de Araujo, Yuri Santos Rego   +1 more
wiley   +1 more source

Strong Kähler with torsion solvable lie algebras with codimension 2 nilradical

Mathematische Nachrichten, Volume 297, Issue 12, Page 4705-4729, December 2024.
Abstract In this paper, we study strong Kähler with torsion (SKT) and generalized Kähler structures on solvable Lie algebras with (not necessarily abelian) codimension 2 nilradical. We treat separately the case of J$J$‐invariant nilradical and non‐J$J$‐invariant nilradical. A classification of such SKT Lie algebras in dimension 6 is provided.
Beatrice Brienza, Anna Fino
wiley   +1 more source

ON DE RHAM AND DOLBEAULT COHOMOLOGY OF SOLVMANIFOLDS [PDF]

Transformation Groups, 2016
23 pages; to appear in Transformation ...
CONSOLE, Sergio, Hisashi Kasuya, FINO, Anna Maria   +2 more
openaire   +2 more sources

Inhomogeneous deformations of Einstein solvmanifolds

Journal of the London Mathematical Society, Volume 109, Issue 5, May 2024.
Abstract For each non‐flat, unimodular Ricci soliton solvmanifold (S0,g0)$(\mathsf {S}_0,g_0)$, we construct a one‐parameter family of complete, expanding, gradient Ricci solitons that admit a cohomogeneity one isometric action by S0$\mathsf {S}_0$. The orbits of this action are hypersurfaces homothetic to (S0,g0)$(\mathsf {S}_0,g_0)$.
Adam Thompson
wiley   +1 more source

Foliation-Preserving Maps Between Solvmanifolds [PDF]

Geometriae Dedicata, 2003
For i = 1,2, let Gamma_i be a lattice in a simply connected, solvable Lie group G_i, and let X_i be a connected Lie subgroup of G_i. The double cosets Gamma_igX_i provide a foliation F_i of the homogeneous space Gamma_i\G_i. Let f be a continuous map from Gamma_1\G_1 to Gamma_2\G_2 whose restriction to each leaf of F_1 is a covering map onto a leaf of ...
Bernstein, Holly, Morris, Dave Witte
openaire   +3 more sources