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Collapse of warped submersions

Collapse of warped submersions

We generalize the concept of warped manifold to Riemannian submersions $\pi:M\to B$ between two compact Riemannian manifolds $(M,g_M)$ and $(B,g_B)$ in the following way. If $f:B\to (0,\infty)$ is a smooth function on $B$ which is extended to a functio