arXiv subjects

Simon Salamon

Publications and source records attributed to Simon Salamon.

25 records · Page 2Linked to original sources

arXiv2003

Complex Product Structures on Lie Algebras

A study is made of real Lie algebras admitting compatible complex and product structures, including numerous 4-dimensional examples. If g is a Lie algebra with such a structure then its complexification has a hypercomplex structure. It is shown in addition that g splits into the sum of two left-symmetric subalgebras. Interpretations of these results are obtained that are relevant to the theory of both hypercomplex and hypersymplectic manifolds and their associated connections.

math.DG↗

arXiv2002

Families of strong KT structures in six dimensions

This paper classifies Hermitian structures on 6-dimensional nilmanifolds M=G/L for which the fundamental 2-form is d d-bar closed, a condition that is shown to depend only on the underlying complex structure J of M. The space of such J is described when G is the complex Heisenberg group, and explicit solutions are obtained from a limacon-shaped curve in the complex plane. Related theory provides examples of various types of Ricci-flat structures.

math.DG↗

arXiv2002

The intrinsic torsion of SU(3) and G_2 structures

We analyse the relationship between the components of the intrinsic torsion of an SU(3) structure on a 6-manifold and a G_2 structure on a 7-manifold. Various examples illustrate the type of SU(3) structure that can arise as a reduction of a metric with holonomy G_2.

math.DG↗

arXiv2001

Complex structures on the Iwasawa manifold

We identify the space of left-invariant oriented complex structures on the complex Heisenberg group, and prove that it has the homotopy type of the disjoint union of a point and a 2-sphere.

math.DG↗

arXiv2001

Anti-self-dual metrics on Lie groups

The aim of the paper is to determine left-invariant,anti-self-dual, non conformally flat, Riemannian metrics on four-dimensional Lie groups.

math.DG↗

arXiv2001

Almost Parallel Structures

A discussion of torsion of Riemannian G-structures leads to a survey of contributions of Alfred Gray and others on almost Hermitian manifolds, G_2-manifolds, curvature identities, volume expansions, plotting geodesics, and the geometry of nilmanifolds. The paper concludes with a new example of a compact 8-manifold with a quaternionic 4-form that is closed but not parallel.

math.DG↗

arXiv2000

Complex structures on nilpotent Lie algebras

We classify real 6-dimensional nilpotent Lie algebras for which the corresponding Lie group has a left-invariant complex structure, and estimate the dimensions of moduli spaces of such structures.

math.DG↗