Nonnegatively curved homogeneous metrics obtained by scaling fibers of submersions

Details Nonnegatively curved homogeneous metrics obtained by scaling fibers of submersions Nonnegatively curved homogeneous metrics obtained by scaling fibers of submersions

2012-03-11

arxiv.org/abs/1203.2371v1

Mathematics

Differential Geometry

23 pages

Scientific paper

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.

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