Noncompact Riemannian spaces with the holonomy group spin\((7)\) and 3-Sasakian manifolds
type: Item
instance of: scholarly article
title: Noncompact Riemannian spaces with the holonomy group spin\((7)\) and 3-Sasakian manifolds
zbMATH Open document ID: 1179.53057
DOI: 10.1134/S0081543808040020
published in: Proceedings of the Steklov Institute of Mathematics
publication date: 2009-10-23T00:00:00Z
review text: The author considers the existence of Riemannian metrics having the special holonomy group \(\text{Spin}(7)\) which smoothly resolve the standard cone metrics on non-compact manifolds and orbifolds related to 7-dimensional 3-Sasakian spaces. This completes his study began in [Sib. Mat. Zh. 48, No.~1, 11--32 (2007); translation in Sib. Math. J. 48, No.~1, 8--25 (2007; Zbl 1164.53360)]. Contents include: Introduction and main results (which contains an overview of the topic); Construction of \(\text{Spin}(7)\)-holonomy metrics; \(\text{Spin}(7)\)-holonomy metrics on \({\mathcal M}_1\); and References.
Mathematics Subject Classification ID: 53C29
Mathematics Subject Classification ID: 53C27
Mathematics Subject Classification ID: 53C10
zbMATH DE Number: 5619787
zbMATH Keywords: non-compact Riemannian spaces
zbMATH Keywords: holonomy group \(\text{Spin}(7)\)
zbMATH Keywords: 3-Sasakian spaces
Wikidata QID: Q115248066
author: Yaroslav V. Bazaikin
reviewed by: Joseph D. Zund
MaRDI profile type: Publication
cites work: On the new examples of complete noncompact Spin(7)-holonomy metrics
cites work: Metrics with exceptional holonomy
cites work: On the construction of some complete metrics with exceptional holonomy
cites work: Compact 8-manifolds with holonomy \(\text{Spin}(7)\)
cites work: New complete noncompact Spin(7) manifolds
cites work: New cohomogeneity one metrics with spin(7) holonomy
cites work: Cohomogeneity one manifolds of spin(7) and \(G_{2}\) holonomy
cites work: M-theory on Spin(7) manifolds
cites work: On spin(7) holonomy metric based on \(\text{SU}(3)/\text{U}(1)\). I
cites work: On spin(7) holonomy metric based on \(\text{SU}(3)/\text{U}(1). \) II
cites work: Weak holonomy groups
cites work: 3-Sasakian manifolds
cites work: Spin(7)-manifolds of cohomogeneity one
cites work: Inhomogeneous Einstein metrics on complex line bundles
full work available at URL: s0081543808040020
OpenAlex ID: W2075486083
description: scientific article; zbMATH DE number 5619787