Any tangent vector field on S^2 has a singular point

Question

Is there an intuitive geometric proof to this?

I don't know exactly what you're looking for, but this might help. — Plutoro, Apr 03 '16 at 00:53

score 2 · Answer 1 · answered Apr 03 '16 at 01:09

2

If a singular point of a tangent vector field $X$ means that $X(x)=0$, your assertion is not true. There exists parallelizable spheres, $S^1,S^3,S^7$ which are the only parallelizable spheres after results of Bott, Kervaire, Milnor.

answered Apr 03 '16 at 01:09

Tsemo Aristide

87,475

Sorry, I meant the S^2 sphere! Thank you – user142702 Apr 03 '16 at 01:10
@user142702, if you meant that, then edit the question to that it means exactly what you mean. – Mariano Suárez-Álvarez Apr 03 '16 at 01:40

Any tangent vector field on S^2 has a singular point

1 Answers1