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Differential Geometry

- Manifolds. Tensors and forms. Connections and curvature. Differential and algebraic topology
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Jan16-12 Greg Bernhardt
Please post any and all homework or other textbook-style problems in one of the Homework & Coursework Questions...
Feb23-13 09:25 AM
1 30,118
Has anyone written on differential geometry for complex spaces where rather than z = x + iy we use z = r e^it (Polar...
Dec3-12 11:49 PM
0 681
Hi All, I'm not a math guy so I am coming to you for help. I am trying to come up with an equation to graph any 180...
Dec3-12 12:06 PM
8 1,701
Hello! I have a problem. How can I convert a left part from picture which is in coordinate system (r, s) to...
Dec3-12 05:30 AM
4 1,334
Hi, Everyone: A way of defining an orientation form when given a codimension-1 , orientable n-manifold N...
Dec2-12 01:12 PM
7 1,719
Hi, All: I'm trying to show that the Mapping torus of a manifold X is a manifold, and I'm trying to see what...
Dec1-12 01:05 AM
7 1,611
Hi, I'm trying to understand the fiber bundle formulation of gauge theory at the moment, and I'm stuck on the...
Nov29-12 09:07 PM
2 993
Hello, I would like to ask you some questions. 1) I've a closed curve (for example an ellipse, which may...
Nov29-12 11:14 AM
3 878
I have a list of points on a 2D simple closed curve and I'd like to approximate that curve using a polynomial such...
Nov28-12 03:10 PM
0 1,051
Hi I'm working on a project where I need to develop a flight path to cover a circular area. I was thinking of having...
Nov28-12 01:29 PM
2 1,050
I been reading some material that lead me to understand that it takes an inner product of a dyad and a vector to...
Nov27-12 11:45 PM
1 998
I have a (3 x N) matrix of column rank 2. If each column is treated as a point in 3-space, then connecting the points...
Nov24-12 12:39 PM
2 1,218
I'm trying to find a reasonably fast method for testing whether or not a point (x,y euclidean coordinate system) lies...
Nov24-12 04:11 AM
3 1,576
If X is a left invariant vector field, then L_x \circ x_t = x_t \circ L_x , where xt is the flow of X and Lx is the...
Nov22-12 05:46 PM
0 1,062
Hello! I came across the following formula for the change in the subtended angle (of a circle), when we move our...
Nov22-12 09:17 AM
0 893
Hairy ball theorem - Wikipedia is not as good or as well-referenced as I'd hoped, and it mainly discusses vector...
Nov21-12 01:19 PM
8 2,122
Hi all, does anyone know if there exists a result that proves/disproves the following?: "If a half-space \{x \in...
Nov21-12 10:18 AM
0 994
Hi, I wish to study (non-trivial) algebraic functions which have varied cycles at a few places other than the...
Nov21-12 09:17 AM
1 1,051
Hi guys, I have a very general question but I would like opinions asap. I am doing a project on Hilbert...
Nov18-12 07:07 PM
1 1,119
Hi, Again: I'm trying to show that, given a 3-manifold M, and a plane field ρ (i.e., a distribution on TM) on M,...
Nov17-12 06:47 AM
11 1,820
Hi, All: There is a standard method to construct a nowhere-zero form to show embedded (in R^n ) manifolds are...
Nov15-12 03:53 PM
8 1,274
hello, I'm trying to understand catmull-clark A. but I'm having a hard time with this...
Nov13-12 06:48 AM
0 965
I've been thinking of a solution, but can't find a one. You have a square of side length 1. You have to draw 2 circles...
Nov12-12 05:40 PM
2 1,049
Hello! I am a bit confused about how I can use covector fields on a differentiable manifold. John M. Lee writes...
Nov12-12 10:10 AM
6 1,632
Hello, can anyone suggest a geometric interpretation of the metric tensor? I am also interested to know how we could...
Nov12-12 09:17 AM
12 2,235
Suppose that points x and y are given in Euclidean space. Point x is displaced to point x1 by x1=x+a(x-y) Given...
Nov12-12 07:27 AM
3 1,040
Hi, All: I need some help with some "technology" on differential forms, please: 1)Im trying to understand...
Nov12-12 07:26 AM
1 902
Hello everyone, I'm studying basic graph theory, and my instructor gives me these statements to translate into...
Nov11-12 07:35 PM
Simon Bridge
1 898
Say I have a function F(x,y)=(f(x),g(y)), F:XY→X'Y'. Is there a theorem that says if f:X→X' and g:Y→Y' are...
Nov9-12 04:15 PM
10 1,543
I am currently reading a paper discussing the convexity of the image of moment maps for loop groups. In particular, if...
Nov9-12 02:32 PM
3 1,089
So I'm having a little trouble with the part of Van Kampen's theorem my professor presented to us. He called this the...
Nov9-12 08:36 AM
4 1,284
If the hyperbolic paraboloid z=(x/a)^2 - (y/b)^2 is rotated by an angle of π/4 in the +z direction (according to...
Nov8-12 11:45 AM
2 1,205
I know that physically, they describe relationships whereby, for instance a vector field, for each point in three...
Nov6-12 03:58 PM
5 1,821
Does anyone have a good book or reference on computing riemannian connections. I'm looking at Do Carmo and can't find...
Nov6-12 03:49 PM
2 1,105
Let S1*(S2*) be the polar cone of the set S1(S2) ( How can I...
Nov4-12 06:14 PM
5 1,385
Hello! I seem to have a problem with spherical coordinates (they don't like me sadly) and I will try to explain it...
Nov3-12 10:00 PM
3 1,871
When given a cylinder with radius, height and thickness, how does one go about computing the amount of material used...
Oct30-12 09:22 PM
1 839
All, I am trying to determine the length of line across 3 dimensions (XYZ). My X&Y are WGS 84 coordinates and my Z...
Oct30-12 03:43 PM
0 851
given a compact, orientable, n-dim. Riemann manifold, what is a sufficient condition for globally vanishing curvature...
Oct30-12 11:36 AM
5 1,316
Suppose a set of k arbitrary points, x_i, 1<=i<=k, x_i from R^2 are selected from a line. How can it be shown that a...
Oct29-12 11:34 AM
6 1,144
Find the vertices of α(t) = 1 - 2 cos(t) I know that to find the vertices we have to set the curvature equal to...
Oct29-12 08:02 AM
2 1,005

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