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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 30,976
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 1,066
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 1,659
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 2,283
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 1,052
Hi, All: I need some help with some "technology" on differential forms, please: 1)Im trying to understand...
Nov12-12 07:26 AM
1 925
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
1 922
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 1,561
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 1,101
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 1,300
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 1,223
I know that physically, they describe relationships whereby, for instance a vector field, for each point in three...
Nov6-12 03:58 PM
5 1,874
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 1,128
Let S1*(S2*) be the polar cone of the set S1(S2) ( How can I...
Nov4-12 06:14 PM
5 1,403
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 1,901
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
1 864
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
0 865
given a compact, orientable, n-dim. Riemann manifold, what is a sufficient condition for globally vanishing curvature...
Oct30-12 11:36 AM
5 1,340
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 1,165
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 1,020
Hi Given is a triangle on points x,y,z in the plane. This triangle has two points a and b on opposite sides (see...
Oct27-12 02:00 AM
7 1,164
prove that for any graph G, kappa (G) ≤delta (G).
Oct27-12 01:14 AM
3 1,112
Can someone please confirm that there is a typo in Nakahara's Geometry, Topology, and Physics, on page 319 (the last...
Oct26-12 12:15 PM
3 1,506
I shall use Seidel's definition of a Liouville domain; in particular, a Liouville domain is a compact manifold M ...
Oct24-12 06:34 AM
1 904
Does anyone know where I can find an algorithm for the points of intersection of two ellipses existing with arbitrary...
Oct23-12 09:34 PM
1 1,608
Hi, I've run into a problem with expanding algebraic functions via Newton polygons. Consider the function: ...
Oct23-12 01:13 PM
5 1,501
Hello, I've just started learning about asymptotes in school. The questions I have are: 1. To find the vertical...
Oct22-12 10:51 AM
1 778
I was working on some algebraic topology matters, thinkgs like the connected sum of some surfaces is some other...
Oct21-12 12:37 AM
5 1,304
I had doubts whether to post this here or in in the physics section but I did here because I'm more interested in a...
Oct20-12 02:56 PM
91 9,730
Let $$M$$ be a surface with Riemannian metric $$g$$. Recall that an orthonormal framing of $$M$$ is an ordered pair of...
Oct20-12 07:24 AM
2 1,036
Hi, You guys know of any (software) function which accepts as input an aribtrary algebraic function, then computes...
Oct18-12 07:53 PM
6 1,560
How do you calculate the Normal vector to an Ellipse. Radius Vector: r=rx*i + ry*j + rz*k Velocity Vector:...
Oct18-12 04:48 PM
15 3,830
Let $$(M,g)$$ be an oriented Remannian surface. Then globally $$(M,g)$$ has a canonical area-2 form $$\mathrm{d}M$$...
Oct18-12 08:34 AM
4 976
Let $$f:U \to \mathbb{R}^3$$ be a surface, where $$U=\{(u^1,u^2)\in \mathbb{R}^2:|u^1|<3, |u^2|<3\}.$$ Consider the...
Oct18-12 03:34 AM
0 747
Hi, I need to do this for some homework and I don't really understand... could anyone help with the following...
Oct17-12 11:14 PM
1 1,027
I'm trying to write an algorithm that will create the smallest possible ellipse to encompass any number of points on...
Oct17-12 11:40 AM
4 1,188
Take for example, the function: a_0(z)+a_1(z)w+a_2(z)w^2+a_3(z) w^3+a_4(z)w^4+a_5(z)w^5=0 with the degree of ...
Oct17-12 06:28 AM
0 851
I am having trouble getting a set definition of what constitutes a manifold for example , I have the real plane...
Oct15-12 11:59 PM
24 2,148
I got these people trying to say that you can orientate a solid oblong so that it looks half the length and width with...
Oct15-12 10:34 PM
Simon Bridge
3 1,147
Suppose I'm given a random function: (-8+5 z+4 z^2)\text{}+(7 z+6 z^4-7 z^5)w+(3 z^2-z^3)w^2+(-8 z-2 z^4-2...
Oct15-12 08:18 AM
0 875
I'm not sure if this is the right forum. I'm actually trying to solve this for a computer program given shape A...
Oct13-12 10:10 PM
1 1,449

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