Results 1 to 10 of about 1,532 (136)

On LCK solvmanifolds with a property of Vaisman solvmanifolds

Complex Manifolds, 2022
The purpose in this paper is to determine a locally conformal Kähler solvmanifold such that the nilradical of the solvable Lie group is constructed by a Heisenberg Lie group.
Sawai Hiroshi
doaj   +3 more sources

Explicit soliton for the Laplacian co-flow on a solvmanifold [PDF]

São Paulo Journal of Mathematical Sciences, 2019
We apply the general Ansatz proposed by Lauret (Rend Semin Mat Torino 74:55–93, 2016 ) for the Laplacian co-flow of invariant $$\mathrm {G}_2$$ G 2 -structures on a Lie group, finding an explicit soliton on a particular almost Abelian 7–manifold.
A. J. Moreno, Henrique N. Sá Earp
semanticscholar   +5 more sources

Einstein solvmanifolds are standard [PDF]

Annals of Mathematics, 2007
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.
J. Lauret
semanticscholar   +7 more sources

Hypercomplex Almost Abelian Solvmanifolds [PDF]

The Journal of Geometric Analysis, 2022
We give a characterization of almost abelian Lie groups carrying left invariant hypercomplex structures and we show that the corresponding Obata connection is always flat.
A. Andrada, M. L. Barberis
semanticscholar   +4 more sources

Inhomogeneous deformations of Einstein solvmanifolds [PDF]

Journal of the London Mathematical Society, Volume 109, Issue 5, May 2024., 2023
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$\mathsf {S}_0$ .
Adam R. Thompson
semanticscholar   +2 more sources

Example of a six-dimensional LCK solvmanifold

Complex Manifolds, 2017
The purpose of this paper is to prove that there exists a lattice on a certain solvable Lie group and construct a six-dimensional locally conformal Kähler solvmanifold with non-parallel Lee form.
Sawai Hiroshi
doaj   +2 more sources

Flat Bundles and Hyper-Hodge Decomposition on Solvmanifolds [PDF]

, 2014
We study rank $1$ flat bundles over solvmanifolds whose cohomologies are non-trivial. By using Hodge theoretical properties for all topologically trivial rank $1$ flat bundles, we represent the structure theorem of K\"ahler solvmanifolds as extensions of
Hisashi Kasuya
openalex   +3 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   +2 more sources

Einstein solvmanifolds: existence and non-existence questions [PDF]

, 2006
The aim of this paper is to study the problem of which solvable Lie groups admit an Einstein left invariant metric. The space $${\mathcal{N}}$$ of all nilpotent Lie brackets on $${\mathbb{R}^n}$$ parametrizes a set of (n + 1)-dimensional rank-one ...
J. Lauret, C. Will
semanticscholar   +3 more sources

Vaisman metrics on solvmanifolds and Oeljeklaus-Toma manifolds [PDF]

, 2012
We prove the non-existence of Vaisman metrics on some solvmanifolds with left-invariant complex structures. By this theorem, we show that Oeljeklaus-Toma manifolds does not admit Vaisman metrics.Comment: 12 page.
Hisashi Kasuya
openalex   +3 more sources