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Differential Geometry

- Manifolds. Tensors and forms. Connections and curvature. Differential and algebraic topology
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Please post any and all homework or other textbook-style problems in one of the Homework & Coursework Questions...
Feb23-13 09:25 AM
1 26,567
Hi, Bernoulli's/Newton's classic elastica equation is of the form: 1) curvature = dθ/ds The RHS reforms to...
May30-12 04:49 AM
6 1,503
So the radius of curvature has a neat geometric "radius of a circle that best approximates the curve" property, but...
May29-12 08:19 PM
0 1,230
I am trying to familiarize myself with the use of fibre bundles and associated bundles but am having some problems...
May29-12 05:45 AM
0 935
I have looked at the definition of the metric tensor, and my sources state that to calculate it, one must first...
May28-12 08:06 AM
17 2,864
I've been trying to calculate the Riemann Curvature Tensor for a certain manifold in 3-dimensional Euclidean Space...
May28-12 07:53 AM
1 1,001
Consider the velocity vector v^i=\dot{x}^i \hat{e}_i . We know that in the plane polar coordinates,it becomes ...
May28-12 02:05 AM
7 1,615
I found the answer and the question now is embarrassing.
May28-12 12:05 AM
1 1,192
I am trying to learn about Holonomy groups. My objective is to read Submanifolds and Holonomy from Berndt, Olmos and...
May27-12 09:05 PM
2 1,330
I was wondering how the indices of tensors work. I do not understand how the indices of tensors in can be used. For...
May26-12 08:09 AM
3 1,481
I am reading Martin Crossley's book - Essential Topology - basically to get an understanding of Topology and then to...
May24-12 05:59 PM
5 1,719
I'm just curious. Let's say a trail designer who works for a Boy Scout camp wants to build two trails that connect...
May24-12 11:07 AM
9 1,953
I have a simple geometry question hopefully I'm posting this in the right forum. I want to draw a simple logarithmic...
May24-12 01:12 AM
2 2,751
Hello all, I have been trying to figure out a clear rule for parallel propagating vectors on spheres, such as in...
May23-12 06:43 AM
13 2,254
How to compute \chi(\mathbb{C}\mathrm{P}^2)? This problem is from a class on differential topology, so we have...
May23-12 12:13 AM
7 1,733
I'm looking for a 'covering rectangle with smaller rectangles' algorithm with the unique feature of being able to...
May22-12 06:03 PM
2 1,336
Hello! I have a question regarding the tangentvector belonging to a parameterized curve, at a certain point p. Lee...
May22-12 04:24 PM
2 1,227
Hi all, I am thinking that, A surface is a minimal surface if and only if the mean curvature is zero. then, for a...
May21-12 02:53 PM
6 1,886
Hi, I'm having trouble interpreting projective transformations. Let's confine ourselves to the projective plane...
May20-12 02:22 PM
5 1,591
As the title suggests, we know from the Abel-Rufini theorem that 5th order equations cannot be solved using radicals....
May20-12 12:31 AM
Stephen Tashi
1 1,202
Is there a way to convert a rational bezier curve to a piecewise series of one or more polynomial bezier curves with...
May20-12 12:28 AM
0 1,229
Let r and a each be a position vector of a point on a plane. Let n be the normal to the plane. The normal equation...
May19-12 03:06 PM
8 1,880
I want to show that the energy displacement of Z^{2n}(r), the 2n-dimensional cylinder with radial radius is at most...
May19-12 01:41 PM
1 928
Given the function: w=\sqrt{(z-5)(z+5)} which is fully-ramified at both the finite singular points and at infinity,...
May19-12 06:38 AM
8 1,786
I would like to read more about this version of simplicial homology and cohomology. Any reference or explanation is...
May18-12 06:02 PM
23 2,664
The plot below is a horn torus. Is that a valid genus-1 normal Riemann surface? I believe it is but I'm just a...
May18-12 06:43 AM
2 1,268
With the help of a few of my friends, we made a problem and was wondering if it is valid. **THIS IS NOT HOMEWORK** ...
May17-12 07:46 PM
0 1,146
in the appendix on Group Theory in Zee's book there is a discussion of commutations for SO(3) two questions -...
May17-12 01:50 PM
1 1,222
Hi all, I am working through Visser's notes...
May16-12 08:44 PM
24 2,727
Hi. I really need an maple program example that solve tensor. Plz help me
May15-12 09:19 AM
1 1,168
Dear all, I am a medical doctor stuck with a mathematics problem. I have taken a project to map the 3D movement of...
May14-12 07:43 AM
11 1,794
hello EveryBody, In the 3D Coordinates I always find 4 parameters instead of 3. A = (X, Y, Z, 1) I wonder...
May13-12 08:58 AM
2 1,083
Hello, I've been looking for solved exercises on graph connectedness, but I can't find any. I'm supposed to compose...
May12-12 01:36 PM
1 1,009
Hello, I have a question regular values and smooth homotopies. Usually in giving the definition of regular value, they...
May11-12 12:49 PM
4 1,156
We say a point x in X (which is a topological space) is an accumulation point of A if and only if any open set...
May11-12 12:30 PM
3 1,469
Hi all, I am trying to follow the derivation by Carroll of the parallel propagator in these notes, beginning page...
May11-12 03:45 AM
3 1,163
Been having trouble with connectedness. Tried out a problem to practice and not sure how to finish it. The problem...
May10-12 09:24 PM
1 1,039
I was told the space S^3 is isomorphic to the set of all 2 component spinors with norm 1 (see...
May10-12 08:36 AM
3 1,371
Hi all, I'm trying to figure out the link between the connection coefficients (Christoffel symbols), the...
May10-12 05:04 AM
5 1,405
Definitions of a rigged Hilbert space typically talk about the "dual space" of a certain dense subspace of a given...
May9-12 08:24 PM
5 1,415
Hi, Can someone here help me understand how to illustrate maps of analytically-continuous paths over algebraic...
May8-12 08:39 AM
5 1,723

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