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A generalization of warped product manifolds with Spin\((7)\) holonomy. (English) Zbl 1221.53083

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) (ISBN 978-0-7354-0546-2/hbk). AIP Conference Proceedings 1023, 165-171 (2008).
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 \(S^2\times S^2\times \mathbb{R}^2\). 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.
For the entire collection see [Zbl 1146.81009].

MSC:

53C29 Issues of holonomy in differential geometry
53C27 Spin and Spin\({}^c\) geometry
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