Results 1 to 10 of about 681 (118)

Einstein solvmanifolds are standard [PDF]

arXiv, 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. Heber has showed that under certain simple algebraic condition called standard (i.e.
Jorge Lauret
arxiv   +7 more sources

Locally conformally Kähler solvmanifolds: a survey [PDF]

Complex Manifolds, 2019
A Hermitian structure on a manifold is called locally conformally Kähler (LCK) if it locally admits a conformal change which is Kähler. In this survey we review recent results of invariant LCK structures on solvmanifolds and present original results ...
Andrada A., Origlia M.
doaj   +8 more sources

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   +2 more sources

Complex and Kaehler structures on compact solvmanifolds [PDF]

Proceedings of the conference on symplectic topology, Stare Jablonki (2004), J. Symplectic Geom. Vol. 3 (2005), 749-767, 2008
We discuss our recent results on the existence and classification problem of complex and Kaehler structures on compact solvmanifolds. In particular, we determine in this paper all the complex surfaces which are diffeomorphic to compact solvmanifolds (and compact homogeneous manifolds in general).
Keizo Hasegawa
arxiv   +3 more sources

Holonomy groups of compact flat solvmanifolds [PDF]

arXiv, 2019
This article is concerned with the study of the holonomy group of flat solvmanifolds. It is known that the holonomy group of a flat solvmanifold is abelian; we give an elementary proof of this fact and moreover we prove that any finite abelian group is the holonomy group of a flat solvmanifold.
Alejandro Tolcachier
arxiv   +3 more sources

Density of the homotopy minimal periods of maps on infra-solvmanifolds [PDF]

arXiv, 2014
We study the homotopical minimal periods for maps on infra-solvmanifolds of type (R) using the density of the homotopical minimal period set in the natural numbers. This extends the result of [10] from flat manifolds to infra-solvmanifolds of type (R). Applying our main result we will list all possible maps on infra-solvmanifolds up to dimension three ...
Jong Bum Lee, Xuezhi Zhao
arxiv   +3 more sources

New supersymmetric vacua on solvmanifolds [PDF]

Journal of High Energy Physics, 2015
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 on the torus.
arxiv   +5 more sources

Modification and the cohomology groups of compact solvmanifolds Ⅱ

Electronic Research Archive
In this article, we refine the modification theorem for a compact solvmanifold given in 2006 and completely solve the problem of finding the cohomology ring on compact solvmanifolds.
Daniel Guan
doaj   +2 more sources

A non-Standard Indefinite Einstein Solvmanifold [PDF]

arXiv
We describe an example of an indefinite invariant Einstein metric on a solvmanifold which is not standard, and whose restriction on the nilradical is nondegenerate.
Federico A. Rossi
arxiv   +2 more sources

Six-dimensional complex solvmanifolds with non-invariant trivializing sections of their canonical bundle [PDF]

arXiv
It is known that there exist complex solvmanifolds $(\Gamma\backslash G,J)$ whose canonical bundle is trivialized by a holomorphic section which is not invariant under the action of $G$. The main goal of this article is to classify the six-dimensional Lie algebras corresponding to such complex solvmanifolds, thus extending the previous work of Fino ...
Alejandro Tolcachier
arxiv   +3 more sources