Please post any and all homework or other textbookstyle problems in one of the Homework & Coursework Questions...

Feb2313 09:25 AM
micromass

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...

Sep1112 11:39 AM
math6

0 
769 
Hello,
the definition of diffeomorphism is: a bijection f:M\rightarrow N between two manifolds, such that both f and...

Sep912 02:22 AM
mnb96

7 
1,183 
I am a physicist trying to understand the notion of holonomy in principal bundles.
I am reading about the...

Sep812 03:49 PM
lavinia

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...

Sep712 11:39 PM
homeomorphic

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....

Sep312 08:21 PM
GPundergrad

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...

Aug3012 05:27 PM
TrickyDicky

7 
2,715 
hello! i'm new over here.. Hope i'm writing where it should be written.
What is the solution of
...

Aug3012 05:12 PM
Mute

5 
2,215 
Say we take N random points in a volume V and connect the points pairwise with linesegments. I would like to estimate...

Aug2912 08:31 PM
Spinnor

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....

Aug2912 08:15 PM
xaos

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...

Aug2912 04:18 PM
AtlasSniperma

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,...

Aug2912 10:30 AM
HallsofIvy

3 
934 
Given a real vector space, I understand the significance of defining a complex structure. Now, if J is a complex...

Aug2812 10:38 PM
chiro

1 
928 
I'm having difficulty understanding the nature of a plane in complex space.
Specifically, I have two complex (N...

Aug2812 05:42 PM
christoff

25 
2,749 
A 180 degree circular arc (i.e. a half sphere) is obvious:
http://i.imgur.com/Upx2A.png
When you rotate this...

Aug2612 12:12 AM
murrdpirate0

2 
1,517 
:cry::cry::cry::cry::cry::cry::cry::cry::cry::cry::cry::cry::cry::cry::cry::cry::cry::cry::cry::cry::cry::cry::cry::cry...

Aug2612 12:07 AM
jedishrfu

2 
1,114 
According to the link below, fractal dimension is an exponent of some sort:...

Aug2512 07:42 AM
HallsofIvy

1 
1,072 
Hello! Could anybody give me some hint with the following problem? Consider a smooth, compact embedded submanifold M =...

Aug2412 05:05 PM
Goklayeh

1 
842 
I have a regular curve, \underline{a}(s), in ℝN (parameterised by its arc length, s).
To a running point on the...

Aug2312 03:05 PM
weetabixharry

7 
1,473 
Exercise #27 from a textbook called Kiselev's Geometry / Book I. Planimetry:
Using only compass, construct a 1...

Aug2312 06:31 AM
coolul007

2 
1,579 
A book I'm reading (Companion to Concrete Math Vol. I by Melzak) mentions, "...any ellipse occurs as a plane section...

Aug2212 05:04 PM
imurme8

2 
953 
Consider a circle of diameter d.
Inscribe a triangle within the circle so that the triangle has hypotenuse d.
...

Aug2212 02:43 PM
zoobyshoe

8 
1,183 
I have recently experimented with algorithms for rendering colour gradients. Linear gradients are no problem, but...

Aug2112 12:18 AM
Ostsol

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...

Aug2012 07:25 PM
QuantumHop

10 
1,489 
I can figure out how to do a rigid rotation in n dimensions. Next I want to look at nonrigid rotations.
Lets...

Aug1912 07:20 AM
lavinia

4 
1,123 
I read some books and see that the definition of covariant tensor and contravariant tensor.
Covariant tensor(rank 2)...

Aug1712 02:20 PM
StationZero

3 
11,067 
In a game I'm developing, I have an ellipse which contains a blue shape inside of it like follows:
...

Aug1612 07:25 PM
chiro

3 
1,109 
If we want to solve $$f(x)=0$$ we can rewrite the equation as
$$g(x)=x$$ and use the fixed point method, i.e,...

Aug1512 02:02 PM
Charles49

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...

Aug1212 08:53 AM
Studiot

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...

Aug1112 07:01 AM
HallsofIvy

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...

Aug912 11:00 AM
mnb96

0 
794 
Hello,
Can anyone explain to me, or tell me a good source where I can find the divergence theorem in a Lorentzian...

Aug812 06:21 AM
PLuz

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 ....

Aug712 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...

Aug712 03:37 PM
sourena

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...

Aug512 09:36 PM
EuphoGuy

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...

Aug512 05:08 PM
meldraft

3 
1,732 
This about those magnetic toys buckyballs. My apologies, I don't really know any physics, so sorry if my terminology...

Aug412 04:33 AM
ImaLooser

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...

Aug112 08:34 PM
lavinia

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...

Aug112 10:14 AM
meldraft

0 
1,150 
A math question about projections of lines: Say we have two straight lines which we consider as number lines...

Jul3112 07:28 PM
imurme8

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...

Jul3112 12:31 AM
chiro

3 
1,165 