Results 11 to 20 of about 1,208 (130)

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

On Low-Dimensional Solvmanifolds [PDF]

Asian J. Math. 20 (2016), no. 2, 199-262, 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. There is an easy criterion for nilpotent Lie groups which enables one to decide whether there is a lattice or not.
arxiv   +5 more sources

Four-dimensional compact solvmanifolds with and without complex analytic structures [PDF]

Complex and Kaehler structures on compact solvmanifolds, J. Symplectic Geom., Vol. 3, No. 4, 2005., 2004
We classify four-dimensional compact solvmanifolds up to diffeomorphism, while determining which of them have complex analytic structures. In particular, we shall see that a four-dimensional compact solvmanifold S can be written, up to double covering, as G/L where G is a simply connected solvable Lie group and L is a lattice of G, and every complex ...
Keizo Hasegawa
arxiv   +3 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

Uniform distribution in solvmanifolds

Advances in Mathematics, 1971
L. Auslander, Jonathan Brezin
openalex   +3 more sources

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 ...
Angella, Daniele, Kasuya, Hisashi
core   +4 more sources

Pseudo-Riemannian Sasaki solvmanifolds [PDF]

, 2022
We study a class of left-invariant pseudo-Riemannian Sasaki metrics on solvable Lie groups, which can be characterized by the property that the zero level set of the moment map relative to the action of some one-parameter subgroup $\{\exp tX\}$ is a normal nilpotent subgroup commuting with $\{\exp tX\}$, and $X$ is not lightlike.
Diego Conti, Federico A. Rossi, Romeo Segnan Dalmasso   +2 more
openalex   +6 more sources

Cohomologically symplectic solvmanifolds are symplectic [PDF]

Journal of Symplectic Geometry, 2011
We consider aspherical manifolds with torsion-free virtually polycyclic fundamental groups, constructed by Baues. We prove that if those manifolds are cohomologically symplectic then they are symplectic. As a corollary we show that cohomologically symplectic solvmanifolds are symplectic.
Hisashi Kasuya
openalex   +6 more sources

The Anosov theorem for exponential solvmanifolds [PDF]

Pacific Journal of Mathematics, 1995
A well-known lower bound for the number of fixed points of a self-map / : X -> X is the Nielsen number N(f). Unfortunately, the Nielsen number is difficult to calculate. The Lefschetz number £(/), on the other hand, is readily computable, but usually does not estimate the number of fixed points.
Edward C. Keppelmann, Christopher McCord
openalex   +3 more sources

Indefinite Nilsolitons and Einstein Solvmanifolds [PDF]

The Journal of Geometric Analysis, 2022
A nilsoliton is a nilpotent Lie algebra $\mathfrak{g}$ with a metric such that $\operatorname{Ric}= \operatorname{Id}+D$, with $D$ a derivation. For indefinite metrics, this determines four different geometries, according to whether $ $ and $D$ are zero or not. We illustrate with examples the greater flexibility of the indefinite case compared to the
Conti D., Rossi F. A.
openaire   +4 more sources