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Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.
2
votes
2
answers
624
views
Independent vector fields
A sequence of vector fields on an open subset of a manifold is linearly independent in module sense, i.e., if we multiply by smooth functions. Does it imply the pointwise independence of the vector fi …
-1
votes
1
answer
328
views
Global invertibility
A differentiable transformation of R^n at each point has an invertible derivative. Does it imply that the transformation is a global diffeomorphism?