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(3+3+2) warped-like product manifolds with Spin(7) holonomy

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Date
2011
Author
Uğuz, Selman
Bilge, Ayşe Hümeyra
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.

Source

Journal of Geometry and Physics

Issue

6

Volume

61

Pages

1093-1103

URI

https://hdl.handle.net/20.500.12469/984
https://doi.org/10.1016/j.geomphys.2011.02.009

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  • Araştırma Çıktıları / Scopus [1565]
  • Araştırma Çıktıları / WOS [1518]
  • Endüstri Mühendisliği / Industrial Engineering [131]

Keywords

Holonomy
Spin(7) manifold
Warped product
Multiply warped product
(3+3+2) warped-like product

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