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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 ×S 2 × 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.
MSC:
53C29Issues of holonomy
53C27Spin and Spin c geometry