Recent content by rych

\frac{\partial n_j}{\partial x^i} = \partial_i \frac{\partial_j \phi}{(\nabla \phi \cdot \nabla \phi)^\frac{1}{2}} = \frac{\partial_{ij}\phi}{(\nabla \phi \cdot \nabla \phi)^\frac{1}{2}} - \frac{\partial_j \phi \sum_k \partial_k \phi \partial_{ik}\phi}{(\nabla \phi \cdot \nabla...

Are there any facts about the derivative of the normalised normal vector n to a surface embedded in n-dimensional Euclid space? Is it true, for instance, that \frac{\partial n_j}{\partial x^i} = \frac{\partial n_i}{\partial x^j} The context is as follows. The surface is defined implicitly by a...