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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 31,147
Let f:X->Y and g:Y->Z be functions. Suppose A is a subset of Z. I'm wondering whether (g o f)-1(A)=f-1(g-1(A)). ...
Sep10-08 01:21 PM
4 2,363
I need to show that every isometry in the plane is a composition of at most three reflections. Now every isometry...
Sep9-08 11:52 PM
19 8,315
I'm having a bit of difficulty proving this, but this is what I have so far: Let a circle with a center O and a...
Sep9-08 04:33 PM
2 3,627
As I understand it a topology on a set X is a collection of subset that satisfy three conditions 1) The collection...
Sep9-08 11:21 AM
7 2,519
Hi everyone, I have struggle to study fuzzy differential geometry for a while and have some difficulties on the...
Sep9-08 03:12 AM
0 1,340
Is the Picard group the same as the group all possible parallel transports on a manifold? If so, is it safe for me to...
Sep8-08 01:10 PM
Jim Kata
0 1,259
Hello all, I am taking a class on differential geometry and I have run into a problem with the following question:...
Sep8-08 12:08 PM
2 1,350
If I stretch an ellipse with .5 eccentricity along an axis 45 degrees from its major axis, doubling its area. How do I...
Sep8-08 08:31 AM
4 6,755
Hi...I'm new to the forum but I need help with the following question. I need to find a topology on N for which...
Sep7-08 08:14 PM
2 1,761
I am trying to show that if X is a topological space, ~ an equivalence relation on X and q:X-->X/~ the quotient map...
Sep6-08 10:46 PM
19 3,067
The wikipedia article on Electromagnetic tensor has: With the electromagnetic tensor, the equations for magnetism...
Sep5-08 04:01 PM
4 4,672
I have this question: Inside a square ABDE, take a point C so that CDE is an isosceles triangle with angles 15...
Sep3-08 09:35 PM
2 1,512
Hi Let's assume we have a, say, 10 cm * 20 cm, not very thick, rectangular object. We also have a huge ball, with a...
Sep2-08 03:14 AM
1 1,353
Hi everyone, i have a problem concerning with the reason to why taking the cycloid to be parametrised by (sin(t)-t,...
Sep1-08 11:31 AM
1 1,885
What is the metric or distance between two points in a hyperbolic space of dimension n?
Sep1-08 03:46 AM
0 1,818
P1: A curve defines a vector at point. P2: A function defines a covector at a point. F1a: A congruence of curves...
Aug30-08 08:03 PM
9 3,041
If three points make a plane? what does four make 1 also until you reach 6 how does that system work?
Aug28-08 07:07 PM
1 5,493
Popular math books usually explain topology as the study of spaces allowing strecthing and shrinking and some cutting...
Aug28-08 04:17 PM
5 2,075
I would like to make visualisations of calabi-yau manifolds, like this...
Aug28-08 04:33 AM
2 2,369
Hi, Easy question about connectedness. I have from Munkres that the finite Cartesian product of connected sets is...
Aug26-08 01:37 PM
1 2,040
Sorry to beat a dead horse. But, maybe; if someone could explain this slowly just using words to me, it would help a...
Aug26-08 12:37 PM
14 2,568
I say what is a functional determinant ?? for example Det( \partial ^{2} + m) is this some kind of Functional...
Aug23-08 12:38 PM
5 4,060
I'm doing a reading of Carroll's General Relativity text, and I am a bit confused about one bit of tensors....
Aug21-08 11:45 AM
5 1,944
Consider f: S1 -> S1: (cos 2 pi x, sin 2 pi x) -> (cos 2 k pi x, sin 2 k pi x). How to show directly from the...
Aug21-08 09:43 AM
1 1,348
I read, again in Spivak's Calculus on Manifolds, that the integral of 1-form over a 1-cube is equivalent to a line...
Aug19-08 01:16 PM
2 2,017
Hi people, I just need to verify that I understand this correctly. For some four dimensional manifold and group...
Aug18-08 01:46 PM
0 1,479
Hi fellas I have been reading Road to Reality by Roger Penrose, but cant go beyond chapter 8. I do not understand...
Aug17-08 12:27 PM
9 1,959
Hey, I posted earlier about the tensor covariant derivative, and the help was great, that makes sense to me now. ...
Aug12-08 11:02 AM
26 9,033
Dear forum-members, Pestered by many (in my opinion, fundamental) questions and no literature at hand to answer...
Aug12-08 10:04 AM
1 2,782
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 22,635
I have a few question, I hope you can help me on some of them. 1.Show that if A (subset of R^n) is a submanifold...
Aug4-08 08:20 AM
3 1,893
I am wondering whether or not anybody has any ideas of how to visualize and calculate the Frechet distance between two...
Aug2-08 02:28 PM
0 2,164
I want to use the theorem that states that if C is the set of critical points in N of a smooth function f:N->M (where...
Aug2-08 11:39 AM
1 1,871
The SO(3) group is topologically a 3-dimensional ball of radius \pi, if the opposite points on its surface are...
Aug2-08 07:28 AM
5 1,934
I'm trying to study some basic tensor analysis on my own for practical purposes, but I'm having some problems. More...
Jul29-08 11:26 AM
6 2,842
Hi, I have a problem with deriving Einstein equations : \epsilon_{IJKL}(e^{I} \wedge R^{JK} + \lambda e^{I}...
Jul27-08 09:27 AM
0 1,618
Hello everyone! I finished school 2 months ago and at the moment I'm looking forward to my study in physics :) ...
Jul26-08 03:48 PM
3 9,935
Hi everybody! I have a question concerning tensors and hope you could help me :) ...
Jul26-08 05:28 AM
11 4,096
Hey all, This question stems from Scorpan, "The Wild World of 4-Manifolds", pg 302 (and all through that...
Jul25-08 11:01 AM
0 1,524
If there is a contravariant vector v=aa+bb+cc with a reciprocal vector system where abc]v=xbc+yac+zab ...
Jul24-08 02:50 AM
1 8,990

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