Lifting Group Actions and Nonnegative Curvature

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We show that all vector bundles over CP^2 which are not spin admit a complete metric with nonnegative sectional curvature. In the proof we construct a nonnegatively curved metric on the corresponding principle bundle by showing that it admits a cohomogeneity one action with singular orbits of codimension 2. This is closely related to the problem of when an action of G on the base of an L principle bundle lifts to the total space, such that the lift commutes with L. We solve this lifting problem for all SO(k) principle bundles over a 4-dimensional simply connected base B with G a cohomogeneity one action on B.
27 pages

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Differential Geometry, 53C29, 53C07

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http://salesiana.dossiersoluciones.com/handle/123456789/145393

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0801.0767
 http://arxiv.org/abs/0801.0767

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arXiv