(3+3+2) warped-like product manifolds with Spin(7) holonomy
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Date
2011
Authors
Bilge, Ayşe Hümeyra
Journal Title
Journal ISSN
Volume Title
Publisher
Elsevier Science Bv
Abstract
We consider a generalization of eight-dimensional multiply warped product manifolds as a special warped product by allowing the fiber metric to be non-block diagonal. We define this special warped product as a (3 + 3 + 2) warped-like manifold of the form M = F x B. where the base B is a two-dimensional Riemannian manifold and the fibre F is of the form F = F-1 x F-2 where the F-i(i = 1 2) are Riemannian 3-manifolds. We prove that the connection on M is completely determined by the requirement that the Bonan 4-form given in the work of Yasui and Ootsuka [Y. Yasui and T. Ootsuka Spin(7) holonomy manifold and superconnection Class. Quantum Gravity 18(2001)807-816] be closed. Assuming that the F-i are complete connected and simply connected it follows that they are isometric to S-3 with constant curvature k > 0 and the Yasui-Ootsuka solution is unique in the class of (3 + 3 + 2) warped-like product metrics admitting a specific Spin(7) structure. Crown Copyright (C) 2011 Published by Elsevier B.V. All rights reserved.
Description
Keywords
Holonomy, Spin(7) manifold, Warped product, Multiply warped product, (3+3+2) warped-like product
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Citation
5
WoS Q
Q2
Scopus Q
Q2
Source
Volume
61
Issue
6
Start Page
1093
End Page
1103