Recent content by badgers14

Thank you, and here is a follow up question that I'm having a little difficulty with. Compute the covariant derivatives \nablau1U and \nablau2U at p=(0,0,0). Where U is the unit normal vector computed in part (a) and with tangent vectors u1=(1,0,0) and u2=(0,1,0). First, I computed U at...

Let M be the surface defined by z=x2+3xy-5y2. Find a unit normal vector field U defined on a neighborhood of p on M. First, I reparameterized the equation for the surface to get x(u,v)=(u,v,u2+3xy-5y2). Next I found two tangent vectors xu(u,v)=(1,0,2u+3v) and xv=(0,1,3u-10v). The next step is...

Can anyone help me with this problem?? Let M be a surface in R^3 oriented by a unit normal vector field U=g1U1+g2U2+g3U3 Then the Gauss map G:M\rightarrow\Sigma of M sends each point p of M to the point (g1(p),g2(p),g3(p)) of the unit sphere \Sigma. Show that the shape operator of M is...