Lie group actions, submanifolds, and warped product submanifolds
How are the smooth group actions and warped product structures in the manifolds?
For example how is the warped product structure in the principal bundle
G \rightarrow M \rightarrow M/G
please give your comment and help
If G acts freely, this is a principal G-bundle over M/G. In general, this need not even be a product locally. eg C^* (nonzero complex numbers) acts on CP^2 giving a 2-implex as a quotient. Look at Kobayashi Nomizu's Differential Geometry book for details on principal bundles.
May be you can find something here on actions of lie group on warped product structure in bundles.
http://wwwf.imperial.ac.uk/~jdg/jmunn-23feb04.pdf
page 26-27
http://www.sciencedirect.com/science/article/pii/S0926224502001080
page 224
http://arxiv.org/pdf/math/0412195.pdf
https://mathematik.uni-heidelberg.de/~banagl/pdfdocs/BanaglFlatBundles.pdf
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