On the infinitesimal automorphisms of quaternionic structures
type: Item
instance of: scholarly article
title: On the infinitesimal automorphisms of quaternionic structures
zbMATH Open document ID: 0829.53029
published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série
publication date: 1995-10-31T00:00:00Z
review text: Let \(G\) be any of the quaternionic linear groups \(\text{GL} (n,\mathbb{H})\), \(\text{GL} (n,\mathbb{H}) \text{Sp} (1)\) or of their compact subgroups \(\text{Sp} (n)\), \(\text{Sp} (n) \text{Sp}(1)\); let \(a (M)\) denote the infinitesimal automorphisms for any of the first two \(G\)-structures and \(a(M,g)\) for any of the last two on a \(4n\)-dimensional manifold \(M\). The comparison between \(a(M)\) and \(a(M,g)\) is discussed on hyperkähler and quaternion Kähler manifolds \(M\). In particular the vanishing of \(a(M)\) is proved on compact quaternion Kähler manifolds with negative scalar curvature and on irreducible compact hyperkähler manifolds. On compact quaternion Kähler \(M\) with positive scalar curvature a formula of Bott type is proved relating the behaviour around the zeros of the infinitesimal automorphisms with the symplectic Pontryagin characteristic numbers.
Mathematics Subject Classification ID: 53C15
Mathematics Subject Classification ID: 53C10
Mathematics Subject Classification ID: 57R20
Mathematics Subject Classification ID: 53C55
Mathematics Subject Classification ID: 53C25
zbMATH DE Number: 811436
zbMATH Keywords: infinitesimal automorphisms
zbMATH Keywords: \(G\)-structures
zbMATH Keywords: quaternion Kähler manifolds
zbMATH Keywords: hyperkähler manifolds
zbMATH Keywords: characteristic numbers
author: Paolo Piccinni
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 811436