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4 votes
1 answer
334 views

Existence parallel vector fields and its effect on the topology of manifolds (Karp's Thesis)

It seems that there is no digital copy of Leon Karp's Ph.D. thesis L. Karp, Vector fields on manifolds, Thesis, New York Univ., 1976. on internet and his paper excerpted from his thesis is very brief ...
C.F.G's user avatar
  • 4,195
2 votes
1 answer
182 views

Vector field along an immersion whose covariant derivative is the differential

Let $(M,g)$ be a Riemannnian manifold and let $f:\Sigma\to M$ be a smooth immersion. Then the vector bundle $f^\ast TM\to\Sigma$ has a natural bundle metric and metric-compatible connection. Can one ...
Quarto Bendir's user avatar