arXiv subjects

Simon G. Chiossi

Publications and source records attributed to Simon G. Chiossi.

6 recordsLinked to original sources

arXiv2026

$η$-Einstein Sasakian Lie algebras

We study $η$-Einstein Sasakian structures on Lie algebras, that is, Sasakian structures whose associated Ricci tensor satisfies an Einstein-like condition. We divide into the cases in which the Lie algebra's centre is non-trivial (and necessarily one-dimensional) and those where it is zero. In the former case we show that any Sasakian structure on a unimodular Lie algebra is $η$-Einstein. As for centreless Sasakian Lie algebras, we devise a complete characterisation under certain dimensional assumptions regarding the action of the Reeb vector. Using this result, together with the theory of normal $j$-algebras and modifications of Hermitian Lie algebras, we construct new examples of $η$-Einstein Sasakian Lie algebras and solvmanifolds, and provide effective restrictions for their existence.

math.DG↗

arXiv2015

Spinorial description of $\mathrm{SU}(3)$- and $G_2$-manifolds

We present a uniform description of $\mathrm{SU}(3)$-structures in dimension $6$ as well as $G_2$-structures in dimension $7$ in terms of a characterising spinor and the spinorial field equations it satisfies. We apply the results to hypersurface theory to obtain new embedding theorems, and give a general recipe for building conical manifolds. The approach also enables one to subsume all variations of the notion of a Killing spinor.

math.DG↗

arXiv2011

Complex homothetic foliations on Kähler manifolds

We obtain a local classification of complex homothetic foliations on Kaehler manifolds by complex curves. This is used to construct almost Kaehler, Ricci-flat metrics subject to additional curvature properties.

math.DG↗

arXiv2011

SO(3)-Structures on 8-manifolds

We study Riemannian 8-manifolds with an infinitesimal action of SO(3) by which each tangent space breaks into irreducible spaces of dimensions 3 and 5. The relationship with quaternionic, almost product- and PSU-geometry is thoroughly explained using representation-theoretical arguments.

math.DG↗

arXiv2005

Special metrics in $G_2$ geometry

We review a recent series of $G_2$ manifolds constructed via solvable Lie groups obtained in math.DG/0409137. They carry two related distinguished metrics, one negative Einstein and the other in the conformal class of a Ricci-flat metric.

math.DG↗

arXiv2004

Conformally parallel G_2 structures on a class of solvmanifolds

Starting from a 6-dimensional nilpotent Lie group N endowed with an invariant SU(3) structure, we construct a homogeneous conformally parallel G_2-metric on an associated solvmanifold. We classify all half-flat SU(3) structures that endow the rank-one solvable extension of N with a conformally parallel G_2 structure. By suitably deforming the SU(3) structures obtained, we are able to describe the corresponding non-homogeneous Ricci-flat metrics with holonomy contained in G_2. In the process we also find a new metric with exceptional holonomy.

math.DG↗