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 Schwachhöfer 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.
%0 Journal Article
%1 Kerr2013
%A Kerr, Megan M.
%A Kollross, Andreas
%D 2013
%J Geometriae Dedicata
%K myown from:kollross
%N 1
%P 269--287
%R 10.1007/s10711-012-9795-0
%T Nonnegatively curved homogeneous metrics obtained by scaling fibers of submersions
%U https://doi.org/10.1007/s10711-012-9795-0
%V 166
%X 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 Schwachhöfer 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.
@article{Kerr2013,
abstract = {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{\"o}fer 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.},
added-at = {2021-07-07T17:07:52.000+0200},
author = {Kerr, Megan M. and Kollross, Andreas},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/29ea2d0772db7de5d42b428be2e69e156/mathematik},
day = 01,
doi = {10.1007/s10711-012-9795-0},
interhash = {ff283a9f353fdba82f7eb5f9e0dd9d06},
intrahash = {9ea2d0772db7de5d42b428be2e69e156},
issn = {1572-9168},
journal = {Geometriae Dedicata},
keywords = {myown from:kollross},
month = oct,
number = 1,
pages = {269--287},
timestamp = {2024-07-20T17:13:18.000+0200},
title = {Nonnegatively curved homogeneous metrics obtained by scaling fibers of submersions},
url = {https://doi.org/10.1007/s10711-012-9795-0},
volume = 166,
year = 2013
}
