\(t\)-conformally semi-plane generalized almost quaternionic manifolds
type: Item
instance of: scholarly article
title: \(t\)-conformally semi-plane generalized almost quaternionic manifolds
zbMATH Open document ID: 0816.53021
author: O. E. Arsen'eva
published in: Russian Mathematics
publication date: 1994-10-05T00:00:00Z
review text: The author introduces a class of manifolds which she calls almost- quaternionic manifolds of a vertical type and considers these manifolds to be a natural generalization of quaternionic-Kählerian manifolds [see \textit{S. Salamon}, Invent. Math. 67, 143-171 (1982; Zbl 0486.53048)]. By definition, if \(\mathbb{H}_ \alpha\) denotes the algebra of generalized quaternions, a subbundle of a tensor bundle \({\mathcal T}^ 1_ 1(M)\) with the typical fibre \(\mathbb{H}_ \alpha\) is called almost-\(\alpha\)- quaternionic structure (\(AQ_ \alpha\)-structure) on a manifold \(M\). In a natural manner the author introduces \(AQ_ \alpha\)-connections, vertical tensors, vertical forms, autodual (self-dual) forms etc. In the same manner, Hermitian \(AQ_ \alpha\)-manifolds are introduced. The twistor curvature of \(AQ_ \alpha\)-manifolds is defined and some properties of this curvature are established. A special case of \(t\)-conformally-flat manifolds is considered. The results are heavily based on the previous work of the author [Generalized almost quaternionic manifolds of vertical type, Deposited at VINITI (Moscow) under no. 58-92, 1991]. Reviewer's remark. In the reviewer's opinion, there are some inaccuracies in the English translation of the paper: e.g. ``body'' instead of ``skew field'', ``semi-plane'' instead of ``semi-flat'', ``autodual'' instead of ``self-dual'' etc.
Mathematics Subject Classification ID: 53C15
Mathematics Subject Classification ID: 53C55
zbMATH DE Number: 640162
zbMATH Keywords: almost-quaternionic manifolds
zbMATH Keywords: quaternionic-Kählerian manifolds
zbMATH Keywords: twistor curvature
zbMATH Keywords: \(t\)-conformally-flat manifolds
MaRDI profile type: Publication
Recommended article: A construction for the existence of a flat induced connection on the structure bundle of an almost quaternionic manifold
Recommended article: Twistor space of a generalized quaternionic Kähler manifold
Recommended article: Q4236868
Recommended article: Q4313400
Recommended article: On the geometry of tensor fields on manifolds with almost quaternion structure
Recommended article: On the geometry of generalized almost quaternionic manifolds of vertical type
Recommended article: The intrinsic torsion of almost quaternion-Hermitian manifolds
Recommended article: Q4869173
Recommended article: Q3822799
Recommended article: Q4441362
description: scientific article; zbMATH DE number 640162