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wofsy
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An oriented surface with a Riemannian metric has a natural action of the unit circle on its tangent bundle. Rotate the tangent vector through the angle theta in the positively direction.
Is there a natural action of SO(n) on the tangent bundle of an oriented Riemannian n-manifold?
Same question for any oriented vector bundle with Riemannian metric over a smooth manifold.
Is there a natural action of SO(n) on the tangent bundle of an oriented Riemannian n-manifold?
Same question for any oriented vector bundle with Riemannian metric over a smooth manifold.
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