differential geometry problem
A catenoid is a surface of revolution. Points in a cateniod, , can be written parametrically as
a. calculate and
b. If a metric on C is defined by where are vector fields tangent to C, show that the components of g relative to the basis for vector fields on C are
ive tried to do the math, but cant get zero, but all
I cant find out how to find these values properly, coz according to my maths wolfram and other are wrong, they a back to front from what i calculated?
c.Use the metric of part b. in Gauss's formula to calculate
d. Using the metric of part b. show that the only non-zero are = = = and . Hence write the geodesic equations on the catenoid. Dont solve them
then form there i have no idea... and i think the other questions are quite wrong...
e.are the v-coordinate curves geodesic curves? [hint use your geodesic equations from d. above]