Nonnegatively curved homogeneous metrics obtained by scaling fibers of submersions

We consider invariant Riemannian metrics on compact homogeneous spaces G/H where an intermediate subgroup K between G and H exists, so that the homogeneous space G/H is the total space of a Riemannian submersion. We study the question as to whether enlarging the fibers of the submersion by a constant scaling factor retains the nonnegative curvature in the case that the deformation starts at a normal homogeneous metric. We classify triples of groups (H,K,G) where nonnegative curvature is maintained for small deformations, using a criterion proved by Schwachh\"ofer and Tapp. We obtain a complete classification in case the subgroup H has full rank and an almost complete classification in the case of regular subgroups.Comment: 23 pages; minor revisions, to appear in Geometriae Dedicat

On symmetries of Chern-Simons and BF topological theories

We describe constructing solutions of the field equations of Chern-Simons and topological BF theories in terms of deformation theory of locally constant (flat) bundles. Maps of flat connections into one another (dressing transformations) are considered. A method of calculating (nonlocal) dressing symmetries in Chern-Simons and topological BF theories is formulated