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Zbl 1221.53083
Bilge, Ayşe H.; Uǧuz, Selman
A generalization of warped product manifolds with Spin$(7)$ holonomy. (English)
[A] Fernandes, Rui Loja (ed.) et al., Geometry and physics. XVI international fall workshop, Lisbon, Portugal, September 5--8, 2007. Melville, NY: American Institute of Physics (AIP). AIP Conference Proceedings 1023, 165-171 (2008). ISBN 978-0-7354-0546-2/hbk

The authors define warped-like product manifolds when the manifold $M$ has fibers which are simply connected and complete, and has a Spin(7) holonomy. They prove that if $M$ has a $3+3+2$ warped-like product, then it is isometric to $S^2\times S^2\times \bbfR^2$. Contents include: An introduction (with a review of previous work); Preliminaries (warped products and their generalization); A generalization of warped product manifolds with Spin$(7)$ holonomy; and a bibliography of ten references. It is indicated that a more extensive discussion will be submitted for publication elsewhere.
[Joseph D. Zund (Las Cruces)]

MSC 2000:: *53C29 Issues of holonomy
53C27 Spin and Spin$^c$ geometry

Keywords: holonomy; Spin$(7)$ manifold; warped products

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