Recent content by Vasileios

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    Graduate Basic diff. geometry question - Gradient of F

    Hi, ok so practically so I can understand this. What is grad(F) for this specific case? Is it as in the Euclidean case (2x,2y)? or it is dependent on some arbitrary tangent vector and the Riemannian metric? I didnt understand your answer completely. Lets try a practical simple example. Say I...
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    Graduate Basic diff. geometry question - Gradient of F

    Hi folks, I have a basic question I would like to ask. I ll start from the Euclidean analogue to try to explain what I want. Suppose we have a smooth function (real valued scalar field) F(x,y)=x^2+y^2, with x,y \in ℝ. We also have the gradient \nabla F=\left( \frac{\partial F}{\partial...
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    Graduate Optimisation along a curve on a surface

    Hi just a further clarification. The actual objective surface F is defined on a Riemmanian manifold W of constant Gaussian curvature. So it is more like in the picture http://img840.imageshack.us/img840/2443/manifoldm.jpg But I can still only move along a line. I cannot chose a direction to get...
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    Graduate Optimisation along a curve on a surface

    Hi everyone, First of all I am not sure if I have chosen the right category for this posting but this looked the most reasonable out. I have a problem that I would like to solve but I am not sure where to look for answers. It seems like something other people might have worked with before...
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    Graduate First fundamental form and squared arc length element

    Hi thanks for the reply. Ok I am a bit confused here. The definition for the first fundamental form I have read about somehow is only defined for manifolds in R3 so I(v,w)= v^T[E F ; F G]w where the coefficients can be written by the Riemannian metric (g_{ij})= [E F ; F G] From that the...
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    Graduate First fundamental form and squared arc length element

    First of all hello, I am new to this forum and I decided to join in order to exchange some information with other members that are more knowledgeable than me in the area of diff. geometry. My background is computer science but I am not a student. I am only now starting to learn about diff...