Conditions on a 1-form allow metric variations on Riemannian submersions with geodesic fibers to achieve positive sectional curvatures on manifold-circle products and to produce fat submersions with non-constant vertizontal curvatures.
Colloque de topologie (espaces fibr´ es), Bruxelles, 1950, 29-55
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Non-canonical variations of Riemannian submersions with totally geodesic fibers
Conditions on a 1-form allow metric variations on Riemannian submersions with geodesic fibers to achieve positive sectional curvatures on manifold-circle products and to produce fat submersions with non-constant vertizontal curvatures.