Properties
The sectional curvature of the target space of a Riemannian submersion can be calculated from the curvature of the total space by O'Neill's formula:
where are orthonormal vector fields on, their horizontal lifts to, is the Lie brackets and is the projection of the vector field to the vertical distribution.
In particular the lower bound for the sectional curvature of is at least as big as the lower bound for the sectional curvature of .
Read more about this topic: Riemannian Submersion
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