- #1
- 7,007
- 10,463
Hi, everyone:
In an effort to show that at any point p in a Riemannian mfld. M
there is an orthonormal basis --relatively straightforward--a new
question came up:
Why aren't the coordinate vector fields always orthonormal?.
I know these are orthonormal when M is locally isometric to
IR^n, but cannot see how?.
We can prove the existence of the orthonormal frames using
Gram-Schmidt. I tried applying Gram-Schmidt to the coord.
V.Fields, see if the projections canceled out, but this is
not working.
Any Ideas?.
Thanks.
In an effort to show that at any point p in a Riemannian mfld. M
there is an orthonormal basis --relatively straightforward--a new
question came up:
Why aren't the coordinate vector fields always orthonormal?.
I know these are orthonormal when M is locally isometric to
IR^n, but cannot see how?.
We can prove the existence of the orthonormal frames using
Gram-Schmidt. I tried applying Gram-Schmidt to the coord.
V.Fields, see if the projections canceled out, but this is
not working.
Any Ideas?.
Thanks.