- #1

Leo Mar

- 3

- 0

I have to prove that the Weingarten Map L for the unit sphere is + or - the identity "by computing the L

_{ik}in a coordinate patch and

**".**

__raising an index__S^2 : x(Φ,θ)=(sinΦcosθ, sinΦsinθ, cosΦ)

I have computed the first (g) and the second (Λ) fundamental forms and I have found :

L=g

^{-1}Λ= ( -1 0 ) = -Identity

_________( 0 -1 )

The plus identity is obtained similarly by choosing a parametrization with inward pointing normal.

But what does "raising an index" mean?

Thank you.