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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 26,458
Dear all, I can formally understand one of the many definitions of tangent vectors to a manifold, but what are they...
Oct17-08 12:12 PM
32 6,298
Hey guys, How exactly do you take the trace of a tensor product? Do I take the trace of each tensor individually...
Nov21-08 06:25 AM
8 6,290
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 6,249
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 6,236
I hope I am posting in the right section. Up to today I was assuming that earth is a sphere, and I was using the...
Nov23-10 02:45 AM
5 6,224
I often think I have fully understood this, then some question comes up in my mind, and I get confused again (which...
Jul10-06 07:03 PM
19 6,179
I've heard of something called a covariant derivative. what motivates it and what is it?
Mar18-07 05:16 PM
12 6,135
one elementary result that you see when you first learn differential geometry is that the pushforward of the Lie...
Jun16-11 10:17 AM
3 6,080
hi, i am trying to prove that \nabla V which has components (\nabla V)^\alpha{}_{\beta} = V^\alpha{}_{;\beta} is...
Oct31-04 09:31 PM
18 6,053
Apr18-07 07:40 AM
7 6,049
I'm looking for a function f: -> R such that |f| and f2 are integrable on any helps?
Feb4-09 06:40 AM
5 6,046
Let A be the adjacency matrix of some graph G. I am aware that A^n counts paths of length n between vertices of G,...
Dec14-09 05:32 PM
0 6,039
I'm currently reading through Roger Penrose's book The Road to Reality and in his Hyperbolic Geometry discussion he...
Aug27-10 11:16 AM
2 6,015
Can a killing vector field generate a diffeomorphism that only shifts points inside a small part of the manifold and...
Mar22-07 10:17 PM
3 6,004
I wonder if anyone might have some suggestions for a good self-study book on tensors. I'm just starting in on Jackson...
Sep1-06 09:15 PM
5 6,002
im looking for a basic high school level geometry book to tech myself from i looked on amazon for a book and i found...
Jul21-09 11:24 AM
Capt. McCoy
2 5,978
im thinking of taking in 2008 the second semester a course in analysis of manifolds. now some of the preliminaries...
Sep11-07 10:51 PM
9 5,930
Is the matrix of a second order symmetric tensor always symmetric (ie. expressed in any coordinate system, and in any...
Apr26-07 10:02 AM
10 5,910
Hi, I'm trying to convert latitude and longitude into meters (x,y). I was thinking of UTM however I don't understand...
Dec5-10 07:19 AM
3 5,895
I've just begun investigating differential forms. I have no experience in this field and no formal, university level...
Jun2-11 03:06 PM
11 5,871
Hello, I'd like to learn about tensors so i can start learning about special relativity. I understand nothing right...
Dec10-06 05:26 PM
16 5,819
Hi! Im trying to get an intuition for these concepts and was just playing at home. My thought was to start with a...
Feb14-12 12:29 AM
23 5,819
Let X be a compact space, (Y,p) a compact metric space, let F be a closed subset of C(X,Y) (the continuous functions...
Feb21-08 01:00 PM
15 5,789
I asked this question in an SR thread started by someone else but it really belongs in this forum. I received much...
Jul4-07 11:17 AM
29 5,786
I'm trying to build up enough understanding to work through some GR on my own, but I'm horribly confused by some of...
Feb5-09 04:25 PM
6 5,777
Being not an expert, my question might sound naive to students of mahematics. My question is how on earth a Lie group...
Jun16-13 02:32 AM
20 5,731
Hi, I am working on a simulation code that simulates the deformation of sand grains in 2D. The sand grains are modeled...
Feb24-09 10:21 PM
6 5,674
Could anybody please give advice for the study of complex analysis, Riemann surfaces & complex mappings. These...
Feb4-08 08:56 PM
3 5,661
Hello. This is 2D with arbitrary orientations. I have a quadratic curve segment defined by 2 end points and another...
Aug26-11 10:26 AM
18 5,654
Hi, everyone: I was just going over some work on Hyperbolic geometry, and noticed that the geodesics in...
Dec9-07 04:23 PM
Chris Hillman
8 5,638
Under which conditions is an inverse of a continuous bijection continuous? I'm not seeking for "the" answer. There...
May17-09 10:34 AM
10 5,635
About the proof of the homology of the Klein Bottle here:...
Mar11-09 02:56 PM
3 5,615
Ok, one more diff geometry question! I need to show the following: Show that if Cij are components of an...
Oct9-08 10:13 AM
32 5,594
I want to make sure of my understanding of coordinate transformations. First of all, is it true that if \ is a...
Dec27-10 03:51 PM
43 5,585
Hello! Could anybody give me an idea about this proof? knowing f_{i}:X\rightarrowR i=1,2 to show whether...
Oct29-08 01:13 PM
3 5,550
In attempting to arrive at a fair critique of Alexander de Seversky's "Combat Plane" concept, I discovered something...
Aug7-11 09:32 AM
24 5,536
Hi, Let \mathbf{x}(u,v) be a local parametrization of a regular surface. Then the coefficients of...
Nov4-07 10:23 PM
Chris Hillman
6 5,533
i don't know if i can post it here, like this man, there's alot...
Oct6-10 05:52 AM
2 5,500
Wald (p. 41) defines a geodesic as a curve whose tangent vector satisfies T^a\nabla_aT^b=0 . . . . . (3.3.1) ...
Feb15-10 10:04 PM
15 5,471
So, where do I begin? I have a current interests in going into Algebraic Topology and I am currently learning about...
Feb7-06 01:42 PM
Doodle Bob
28 5,445

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