View the step-by-step solution to:

Let v , w, and y be dierentiable vector elds in U S, f : U R be dierentiable functions in S , y (f ) be the derivative of f in the direction of y and...

See attachment. Problem 1

Let v , w , and y be differentiable vector fields in U S,f : U R be differen- tiable functions in S , y ( f ) be the derivative of f in the direction of y and a , b be real numbers. Show that the covariant derivative has the following property D y ( fv ) = y ( f ) v + fD y ( v ) 1
Background image of page 1

Top Answer

Dear student, please... View the full answer


Let assume that c be a differentiable curve with c(t0 ) = p and with
= y (p) Then
Dy (f v ) = f (c(t)).v (c(t))
df (c(t))
dv (c(t))
.v (c(t)) + f (c(t)).
= y (f ).v + f.Dy (v ) dc

Sign up to view the full answer

Why Join Course Hero?

Course Hero has all the homework and study help you need to succeed! We’ve got course-specific notes, study guides, and practice tests along with expert tutors.


Educational Resources
  • -

    Study Documents

    Find the best study resources around, tagged to your specific courses. Share your own to gain free Course Hero access.

    Browse Documents
  • -

    Question & Answers

    Get one-on-one homework help from our expert tutors—available online 24/7. Ask your own questions or browse existing Q&A threads. Satisfaction guaranteed!

    Ask a Question
Ask a homework question - tutors are online