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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 30,955
Say we have open sets from two topological spaces. A is an open subset of T1 and B is an open subset of T2. So for...
Sep25-08 09:45 PM
1 4,262
I have a question about complex projective space... specifically CP1 which can be thought of as the action of C on...
Oct11-08 11:51 AM
1 1,343
I am the captain of my schools academic team. One of the main topics this year is Spherical trig and I can't find out...
Mar13-09 08:12 AM
5 1,819
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 1,443
The following was given as an intuitive explanation of understanding why a sphere's area is four times the area of the...
Sep12-12 06:25 AM
1 1,391
I'm doing some programing and I am wondering how I can find the length of a Polygon's side (variable number of sides)...
Sep15-08 03:36 PM
2 7,708
Hello, I need help. The topic is a gradient in spherical coordinates. In cartesian it is clear but in spherical...
Aug9-08 05:00 PM
3 22,602
I am confused on what is meant by the modulus of a Riemann surface. I have done some very quick searches through my...
Jun4-12 11:04 PM
9 1,359
I have been working on something in my spare time and I have to graph the particle's motion in three dimensions...
May15-11 05:40 PM
4 4,369
I am trying to turn a 3D parametric equation into a vector field for an experiment, but I am not having much luck. =...
May17-11 03:54 AM
2 1,764
Let h = det h_{alpha beta}. The number of dimensions is not necessarily four. Show that \ delta h is the...
Jan16-06 05:07 AM
1 3,608
Hey guys. I am trying to find a shape that suits my needs. The amount of vertexes can be any, but the fewer the...
Jan6-12 09:03 AM
5 1,209
I would like to explore writing differential geometry in matrix format and was wondering if any of the experts here...
Nov22-09 10:27 AM
3 1,459
Does anyone know what the metric tensor looks like for a 2 dimensional sphere (surface of the sphere)? I know...
Jun25-11 03:48 PM
2 1,686
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
0 690
An ellipse is a conic section. If you construct an ellipse using a cone, does the axis of the cone cross through one...
Dec8-08 02:33 AM
3 3,379 It is known that simple perfect squared squares exist, with the lowest...
Feb21-12 03:53 PM
6 1,550
Hello guys, I keep hearing that Euclidean parallel postulate was broken through differential geometry, can someone...
Aug31-09 01:24 PM
20 3,027
I have a sphere with the equation (x-3)2+(y-2)2+(z+5)2=36 two question: 1. how do I find the equation of the...
Jan25-10 07:50 AM
1 5,271
I was talking to a friend recently about the nature of infinity and Georg Cantor's Continuum Hypothesis and I recanted...
May26-10 11:59 AM
2 961
I was wondering if topology has ever been utilized on the structure of DNA and how that applies to its functions? I am...
Sep8-10 12:18 PM
2 833
I need some help getting from point A to B. Let's say we have the plain ol' heat equation u_t=\Delta u where the...
Dec22-05 04:48 PM
3 1,868
OK, this is more of a spot for an elaboration on a question I just posted in another thread. Not quite duplicating...
Feb1-06 08:46 AM
5 6,481
Hi I'm looking for a simple definition fo the affine connection because I can't understand it's meanning , that...
Apr9-08 01:55 PM
12 7,036
Hi , everyone I have a problem with geodesic equation . I know the method of solving it , but I can't understand the...
Apr15-08 05:21 PM
the shadow
14 6,928
I find that group structure of n-sphere is SO(n+1)/SO(n) (at So I want to find...
Mar22-12 10:12 PM
7 1,496
Prove the theorem (Appolonius) for the triangle ABC where A, B, C are the respective points (-a,0), (a,0), (b,C) on...
Jun18-07 05:41 PM
2 1,869
Hello members, I am a bit stumped on a mathematical problem. If this is in the wrong section I apologize. ...
Oct8-10 06:51 AM
0 921
How many independant components does the Riemann-Tensor have in n- dimensional space?
Apr8-07 06:04 PM
Chris Hillman
5 5,269
What is the metric or distance between two points in a hyperbolic space of dimension n?
Sep1-08 03:46 AM
0 1,813
There are models I've come across in physics involving things such as a 4 dimensional surface of a 5 dimensional...
Sep13-10 07:35 PM
21 2,829
For n\geq 2, is there a smooth map f: S^n\rightarrow E (E is the equator of S^n) which has the property that the...
Sep30-09 07:52 PM
2 1,645
Using the Mayer–Vietoris sequence, how can we calculate the De Rham cohomology of the Kelin bottle?
Oct15-09 09:17 AM
8 3,584
How can we prove that the tensor product between two tensors of lower rank forms the basis for ANY tensor of higher...
Feb24-07 12:02 AM
37 4,281
what is a good book in differential geometry. I currently know calculus, a bit about differential equations, a bit of...
Feb28-07 03:16 PM
2 1,900
how do we derive the formula for the parallel tranport of a general tensor? I understand the ones for covarint and...
Mar18-07 06:05 PM
0 1,434
i'm having a hard time computing these so could people show me several examples to help me get a better feel for them...
Mar24-07 04:22 AM
7 18,430
What exactly is the exterior derivative? What is its motivation? how do you compute it? Most importantly why is that...
May24-10 03:28 PM
18 5,145
i was curious as to what exactly this is and more importantly, what motivates it. what are its applications?
Jun13-10 04:27 AM
35 15,914
what are they exactly?
Apr24-07 02:26 PM
1 1,169

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