Special warped-like product manifolds with [G.sub.2] holonomy

By using the fiber-base decompositions of manifolds, the definition of warped-like product is regarded as a generalization of multiply warped product manifolds, by allowing the fiber metric to be not block diagonal. We consider the (3 + 3 + 1) decomposition of 7-dimensional warped-like product manif...

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Bibliographic Details
Published in:Ukrainian mathematical journal 2014-01, Vol.65 (8), p.1257
Main Author: Uguz, S
Format: Article
Language:English
Subjects:
Fibers
Online Access:Get full text
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Summary:By using the fiber-base decompositions of manifolds, the definition of warped-like product is regarded as a generalization of multiply warped product manifolds, by allowing the fiber metric to be not block diagonal. We consider the (3 + 3 + 1) decomposition of 7-dimensional warped-like product manifolds, which is called a special warped-like product of the form M = F x B, where the base B is a one-dimensional Riemannian manifold and the fiber F has the form F = [F.sub.1] x [F.sub.2] where [F.sub.i], i = 1,2, are Riemannian 3-manifolds. If all fibers are complete, connected, and simply connected, then they are isometric to [S.sup.3] with constant curvature k > 0 in the class of special warped-like product metrics admitting the (weak) [G.sub.2] holonomy determined by the fundamental 3-form.
ISSN:0041-5995