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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 26,438
let x a point on complex manifold X, z_j a coordinate system at x , E a holomorphic bundle and let h_α be a...
Sep11-12 11:39 AM
0 769
Hello, the definition of diffeomorphism is: a bijection f:M\rightarrow N between two manifolds, such that both f and...
Sep9-12 02:22 AM
7 1,183
I am a physicist trying to understand the notion of holonomy in principal bundles. I am reading about the...
Sep8-12 03:49 PM
3 1,822
Just like the title says, what is a dual vector. I am reviewing Panton's "Incompressible Flow", Chapter 3, and a brief...
Sep7-12 11:39 PM
9 2,151
Hello all, this is my first topic here at PF, though I have been using this site as a homework aid for quite a while....
Sep3-12 08:21 PM
6 2,329
Hello, So, given two points, x and x', in a Lorentzian manifold (although I think it's the same for a Riemannian...
Aug30-12 05:27 PM
7 2,715
hello! i'm new over here.. Hope i'm writing where it should be written. What is the solution of ...
Aug30-12 05:12 PM
5 2,215
Say we take N random points in a volume V and connect the points pairwise with line-segments. I would like to estimate...
Aug29-12 08:31 PM
2 1,308
Here is the problem: If M is a manifold with boundary, then find a retraction r:U→∂M where U is a neighborhood of ∂M....
Aug29-12 08:15 PM
2 910
Hey folks, Bit of a complex question here, but I'm hoping someone smarter than myself can help me figure this out. I...
Aug29-12 04:18 PM
2 1,143
Would someone here be able to write down for me an example of a metric on a manifold with both macroscopic dimensions,...
Aug29-12 10:30 AM
3 934
Given a real vector space, I understand the significance of defining a complex structure. Now, if J is a complex...
Aug28-12 10:38 PM
1 928
I'm having difficulty understanding the nature of a plane in complex space. Specifically, I have two complex (N...
Aug28-12 05:42 PM
25 2,749
A 180 degree circular arc (i.e. a half sphere) is obvious: When you rotate this...
Aug26-12 12:12 AM
2 1,517
Aug26-12 12:07 AM
2 1,114
According to the link below, fractal dimension is an exponent of some sort:...
Aug25-12 07:42 AM
1 1,072
Hello! Could anybody give me some hint with the following problem? Consider a smooth, compact embedded submanifold M =...
Aug24-12 05:05 PM
1 842
I have a regular curve, \underline{a}(s), in ℝN (parameterised by its arc length, s). To a running point on the...
Aug23-12 03:05 PM
7 1,473
Exercise #27 from a textbook called Kiselev's Geometry / Book I. Planimetry: Using only compass, construct a 1...
Aug23-12 06:31 AM
2 1,579
A book I'm reading (Companion to Concrete Math Vol. I by Melzak) mentions, "...any ellipse occurs as a plane section...
Aug22-12 05:04 PM
2 953
Consider a circle of diameter d. Inscribe a triangle within the circle so that the triangle has hypotenuse d. ...
Aug22-12 02:43 PM
8 1,183
I have recently experimented with algorithms for rendering colour gradients. Linear gradients are no problem, but...
Aug21-12 12:18 AM
1 1,146
Not sure if this is a topology question but here goes. Imagine an infinitely long piece of string and I cut it in...
Aug20-12 07:25 PM
10 1,489
I can figure out how to do a rigid rotation in n dimensions. Next I want to look at non-rigid rotations. Lets...
Aug19-12 07:20 AM
4 1,123
I read some books and see that the definition of covariant tensor and contravariant tensor. Covariant tensor(rank 2)...
Aug17-12 02:20 PM
3 11,067
In a game I'm developing, I have an ellipse which contains a blue shape inside of it like follows: ...
Aug16-12 07:25 PM
3 1,109
If we want to solve $$f(x)=0$$ we can re-write the equation as $$g(x)=x$$ and use the fixed point method, i.e,...
Aug15-12 02:02 PM
3 1,195
Knowing the initial point of a vector (X1,Y1) and its magnitude and angle (R,θ) HOW CAN I CALCULATE ITS FINAL POINT...
Aug12-12 08:53 AM
7 2,234
If we have a unit circle within a square s.t. the square touches the circle in 4 places then the biggest gap we can...
Aug11-12 07:01 AM
11 1,844
Hello, let's suppose I have the following system of curvilinear coordinates in ℝ2: x(u,v) = u y(u,v) = v + e^u where...
Aug9-12 11:00 AM
0 794
Hello, Can anyone explain to me, or tell me a good source where I can find the divergence theorem in a Lorentzian...
Aug8-12 06:21 AM
0 884
hi friends, Suppose we have a vector bundle E equipped with a hermitian metric h, and in a subbundle of E noted SE ....
Aug7-12 07:57 PM
Ben Niehoff
1 950
How can I calculate degrees of freedom of a rank (o,3) tensor, Aabc, that is mixed symmetry and antisymmetric in the...
Aug7-12 03:37 PM
3 1,213
Hello all, this is my first time posting on this forum, so to start with, it's good to meet you all and thanks in...
Aug5-12 09:36 PM
0 804
Suppose I have a vector space. There is circle with center at the origin of the vector space. There is also a line L...
Aug5-12 05:08 PM
3 1,732
This about those magnetic toys buckyballs. My apologies, I don't really know any physics, so sorry if my terminology...
Aug4-12 04:33 AM
1 1,114
Consider the unit ball B:=B_1(0)\subset \mathbb{R}^2. How can one prove that the set B\times B \setminus D, where...
Aug1-12 08:34 PM
2 931
Ok, so I'm trying to plot the unit circle using the chebyvhev metric, which should give me a square. I am trying this...
Aug1-12 10:14 AM
0 1,150
A math question about projections of lines: Say we have two straight lines which we consider as number lines...
Jul31-12 07:28 PM
0 785
Not much. Im not sure where to put this so mods move it as need Anyways here is the back story, We have been...
Jul31-12 12:31 AM
3 1,165

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