Oct 1, 2018
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20121115 Differential Manifolds, topics covered; LMU, Winter 2012
20121115, Prof. Leeb.
I.4.6. Submersions and immersions
After having defined the differential, we can generalize these notions to the setting of manifolds.
Def. submersion, immersion, embedding. Immersions are locally embeddings.
Prop. immersion is embedding iff homeomorphism onto image.
Corollary: If M compact, every injective immersion is an embedding.
I.5. Vector fields, flows, Lie brackets
integral curves, lots of references to local theory of ODEs
globally obtain, uniqueness of local solutions, unique maximal integral curve