Results 1 to 10 of about 1,691 (152)
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 +9 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 +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 in geometric flows on homogeneous spaces proposed by Jorge Lauret for the Laplacian co-flow of invariant $G_2$-structures on a Lie group, finding an explicit soliton on a particular almost Abelian $7$-manifold.Comment: Minor ...
Earp, Henrique N. Sá +1 more
core +5 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 +6 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
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
On the rationality of the Nielsen zeta function for maps on solvmanifolds [PDF]
arXiv, 2022 In [3,9], the Nielsen zeta function $N_f(z)$ has been shown to be rational if $f$ is a self-map of an infra-solvmanifold of type (R). It is, however, still unknown whether $N_f(z)$ is rational for self-maps on solvmanifolds. In this paper, we prove that $N_f(z)$ is rational if $f$ is a self-map of a (compact) solvmanifold of dimension $\leq 5$.
K. Dekimpe, I. V. Bussche
arxiv +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
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
Small Covers, infra-solvmanifolds and curvature [PDF]
, 2018 It is shown that a small cover (resp. real moment-angle manifold) over a simple polytope is an infra-solvmanifold if and only if it is diffeomorphic to a real Bott manifold (resp. flat torus). Moreover, we obtain several equivalent conditions for a small
Kuroki, Shintarô +2 more
core +2 more sources