- #1

- 2

- 0

I (at least very roughly) understand the relationship between the Frenet-Serret curvature of a curve and the Riemann curvature of a general n-dimensional manifold: the curvature tensor is determined by the sectional curvatures of 2-D slices through the manifold, and Gauss's theorem relates these sectional curvatures to the curvature of curves along the two principal directions of the 2-D surface.

What I was wondering was is there a similar geometric relationship between the Frenet-Serret torsion of curves and the torsion tensor for a general manifold, and if so are there any good sources for reading about it?

Thanks,

Lucy