Collapse of warped submersions
Szymon M. Walczak (2006)
Annales Polonici Mathematici
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We generalize the concept of warped manifold to Riemannian submersions π: M → B between two compact Riemannian manifolds and in the following way. If f: B → (0,∞) is a smooth function on B which is extended to a function f̂ = f ∘ π constant along the fibres of π then we define a new metric on M by , where and denote the bundles of horizontal and vertical vectors. The manifold obtained that way is called a warped submersion. The function f is called a warping function. We show...