0

Does someone know how to define curvature of a one dimensional riemannian manifold (without a ambient space)? A particular case is to define curvature of a curve embedded in $\mathbb{R}^n$ as a submanifold with the induced euclidean metric for $n \geq 4$.

flag
3 
 You should ask this on math.stackexchange.com and not here. And are you studying differential geometry from a textbook? Perhaps you should find one that discusses specifically curves and surfaces in R^3. The generalization to higher dimensional Euclidean space is straightforward. – Deane Yang Feb 8 at 20:56
2 
 ...for instance, do Carmo "Differential geometry of curves and surfaces". Most undergraduate-level differential geometry textbooks would cover this. – Misha Feb 8 at 21:09
but, it always makes use of a ambient space. I think the question is deeper and it is not treated in a book like do Carmo "Riemannian Geometry". – Guilherme Feb 9 at 11:16

closed as off topic by Deane Yang, Misha, MTS, Alexandre Eremenko, Mark Meckes Feb 9 at 2:41

Browse other questions tagged or ask your own question.