# Search results

1. ### A Cross Product Matrix

I am not following. I should have said: assuming that the Levi Civita 3x3x3 matrix would have to remain the same for orthogonal curvilinear coordinates. That's my own thought as I knew I had to somehow generate the same velocity vector. And I think the article confirms my thinking; I quoted it...
2. ### A Cross Product Matrix

If given a position vector defined for a orthogonal curvilinear coordinate system HOW would the matrices that make up the Levi Civita 3x3x3 matrix remain the same? "Levi Civita 3x3x3 is said to be independent of any coordinate system or metric...
3. ### A Theory of Surfaces and Theory of Curves Relationship

Oh ok! So the sphere's gradient vector would point in the same direction as the circle's negative normal vector?
4. ### A Theory of Surfaces and Theory of Curves Relationship

Ok Why doesn't the normal to space curve contained on a surface not point in the same direction as that surfaces normal vector (gradient)?
5. ### A Theory of Surfaces and Theory of Curves Relationship

Hello I am interested in the Frenet-Serret Formulas (theory of curves?) relationship to theory of surfaces. 1) Can one arrive to the Frenet-Serret Formulas starting from the theory of surfaces? Any advice on where to begin? 2) For a surface that contain a space curve: if the unit tangent...