- #1
kiuhnm
- 66
- 1
I'm learning Differential Geometry on my own for my research in ML/AI. I'm reading the book "Gauge fields, knots and gravity" by Baez and Muniain.
An exercise asks to show that "if [itex]\phi:M\to N[/itex] we can push forward a vector field [itex]v[/itex] on [itex]M[/itex] to obtain a vector field [tex](\phi_*v)_q = \phi_*(v_p)[/tex] whenever [itex]\phi(p)=q[/itex]."
I get a [itex]q[/itex] in both places:
[tex](\phi_*v)_q(f) = (\phi_*v)(f)(q) = (v(f\circ \phi))(q) = v_q(f\circ \phi)=(\phi_* v_q)(f)[/tex]
What's wrong with my steps?
An exercise asks to show that "if [itex]\phi:M\to N[/itex] we can push forward a vector field [itex]v[/itex] on [itex]M[/itex] to obtain a vector field [tex](\phi_*v)_q = \phi_*(v_p)[/tex] whenever [itex]\phi(p)=q[/itex]."
I get a [itex]q[/itex] in both places:
[tex](\phi_*v)_q(f) = (\phi_*v)(f)(q) = (v(f\circ \phi))(q) = v_q(f\circ \phi)=(\phi_* v_q)(f)[/tex]
What's wrong with my steps?