Results 11 to 20 of about 1,537 (138)

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.
Jorge Lauret
semanticscholar   +7 more sources

Hypercomplex Almost Abelian Solvmanifolds [PDF]

The Journal of Geometric Analysis, 2023
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.
Adrián Andrada, M. L. Barberis
semanticscholar   +4 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

On Low-Dimensional Solvmanifolds [PDF]

Asian Journal of Mathematics, 2009
A nilmanifold resp. solvmanifold is a compact homogeneous space of a connected and simply-connected nilpotent resp. solvable Lie group by a lattice, i.e. a discrete co-compact subgroup.
Christoph Bock
semanticscholar   +5 more sources

Indefinite Nilsolitons and Einstein Solvmanifolds [PDF]

The Journal of Geometric Analysis, 2021
A nilsoliton is a nilpotent Lie algebra $$\mathfrak {g}$$ g with a metric such that $${{\,\mathrm{Ric}\,}}=\lambda \mathrm {Id}+D$$ Ric = λ Id + D , with D a derivation.
D. Conti, F. Rossi
semanticscholar   +6 more sources

New supersymmetric vacua on solvmanifolds [PDF]

Journal of High Energy Physics, 2016
We obtain new supersymmetric flux vacua of type II supergravities on four-dimensional Minkowski times six-dimensional solvmanifolds. The orientifold O4, O5, O6, O7, or O8-planes and D-branes are localized. All vacua are in addition not T-dual to a vacuum
Andriot, David
core   +6 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.
Jonathan Brezin
semanticscholar   +5 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

Inhomogeneous deformations of Einstein solvmanifolds [PDF]

Journal of the London Mathematical Society, Volume 109, Issue 5, May 2024., 2023
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   +2 more sources

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

, 2010
The general aim of this paper is to study which are the solvable Lie groups admitting an Einstein left invariant metric. The space N of all nilpotent Lie brackets on R^n parametrizes a set of (n+1)-dimensional rank-one solvmanifolds, containing the set ...
Lauret, Jorge, Will, Cynthia
core   +2 more sources