I am aware of circles of curvature and I am simply wondering to what extent does this generalize to $n$-dimensions. Specifically, if some surface in $n$-dimensional space is represented parametricaly, how does one determine the $n$-sphere of curvature at any given point?
How does one determine $n$-spheres of curvature?
5
$\begingroup$
calculus
analysis
differential-geometry
-
0Space curves do have osculating spheres and osculating circles (the circle formed by the intersection of the osculating sphere and osculating plane). – 2011-09-13