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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 31,063
In Frankel's book he writes that in R^{3} with cartesian coordinates, you can always associate to a vector \vec{v} a...
T 09:14 AM
Greg Bernhardt
1 198
Hey JO, I'm reading a book on geometric algebra and in the beginning (there was light, jk) a simple calculation is...
Y 03:33 PM
5 228
Does anybody know nice introductory material for K3 manifold/ surface? Some very basic exposition, maybe hidden in...
Aug24-14 12:35 AM
2 2,130
Let me say from the beginning I'm not talking about the non-coordinate unit vectors for polar coordinates. I'm talking...
Aug22-14 08:40 PM
3 194
Alright, so I was reading up on tensors and such with non-Cartesian coordinate systems all day but now I'm a bit tired...
Aug22-14 07:53 AM
5 187
What are tensors?
Aug21-14 02:03 PM
6 413
Hello. I'm learning about Lie derivatives and one of the exercises in the book I use (Isham) is to prove that given...
Aug21-14 05:50 AM
5 235
i really try understand these initial concepts before continue my work, The necessity to use contra/covariants...
Aug20-14 02:15 PM
5 269
i'm looking for a curve that would have a shape of a snowdrop (the white spring flower) in 3D space. i have tried some...
Aug20-14 05:19 AM
2 197
Hi all, I am trying to describe/understand how to define a 2-plane distribution in R^3 , i.e., an assignment of a...
Aug20-14 03:51 AM
Pond Dragon
3 211
Hello I've been reading some Group theory texts and would like to clarify something. Let's say we have two Lie groups...
Aug18-14 01:27 PM
2 236
Dear all, I was revising on a bit of tensor calculus, when I stumbled upon this: $$\delta^i_j = \frac{\partial...
Aug16-14 01:32 PM
2 237
I have a cluster of voxels and a 2nd order stress tensor corresponding to each voxel. I was wondering as to what would...
Aug15-14 05:19 PM
1 210
does anyone have a proof of this?
Aug14-14 07:00 PM
2 355
The Maurer-Cartan one-form ##\Theta = g^{-1} dg## is though of as a lie algebra valued form. It arises in connection...
Aug12-14 03:57 PM
Greg Bernhardt
1 466
Hi, I have real problems with the indices here, can someone give me a step by step explanation how to compute stuff...
Aug12-14 03:07 PM
5 1,003
Can somebody explain to me what is a manifold.Also what it means for a space to be curved and how we define...
Aug11-14 05:05 PM
12 773
Hello, the tensor product definition of a two form is \alpha^{1} \wedge \beta^{1} := \alpha \otimes \beta - \beta...
Aug8-14 06:26 PM
10 409
In the formulation of connections on principal bundles, one derives an expression for the covariant exterior...
Aug7-14 11:41 AM
center o bass
4 353
I have an object (A) at some altitude above the Earth ellipsoid, and a point (B) on the surface of the Earth. ...
Aug6-14 12:11 AM
6 910
Hi all, I'm trying (and failing miserably) to understand tensors, and I have a quick question: is the inner product...
Aug4-14 11:17 AM
4 502
It is pretty straight forward to prove that the Kronecker delta \delta_{ij} is an isotropic tensor, i.e. rotationally...
Aug1-14 08:32 PM
6 530
Hi, I'm giving a talk tomorrow morning, and I'd like to use the following fact: a path-connected subgroup of SO(3)...
Jul31-14 12:05 PM
3 444
I finally finished my big summer research project. Reviewing how it went, it is clear to me that I lack an...
Jul24-14 09:14 PM
Pond Dragon
1 1,247
Hey guys, I'm working on a summer research project right now in diff. geo. I'm at the point where I have to define the...
Jul23-14 11:35 PM
Greg Bernhardt
1 2,101
In Nakahara's book, the interior product is defined like this : i_{x} \omega = \frac{1}{r!} \sum\limits_{s=1}^r...
Jul22-14 07:50 PM
11 2,579
I wonder if curvature necessarily means space has been removed. The typical example is forming a "curved" surface by...
Jul22-14 02:31 AM
9 990
(From another site) I think the answer is no, for ##i: S \rightarrow \mathbb R^n ## the inclusion/restriction, and...
Jul18-14 05:48 PM
3 1,477
I'm trying to explicitly show that \varepsilon^{0 i j k} \varepsilon_{0 i j l} = - 2 \delta^k_l I sort of went...
Jul18-14 09:11 AM
2 1,409
Long time reader, first time poster. Originally, it was my contention that all Lie groups could be written as the...
Jul17-14 10:36 PM
Pond Dragon
1 1,381
I need to use a computational software to work on tensorial hermite polynomials. The operations I want to perform are...
Jul9-14 08:46 AM
3 3,169
Hello, I'm trying to get a hang of the defintion presented in Arfken - Mathematical Methods for Physicists for 3...
Jul8-14 02:46 AM
2 1,967
I am working on a paper that provides the following formula for computing radius of curvature at a point on a surface....
Jul4-14 10:39 AM
1 3,493
I'm reading about multlinear algebra and I'm stuck at differential form and outer product. The definitions involve...
Jul4-14 12:33 AM
13 4,267
Greetings, I am attempting to compute geodesic distances on manifolds where structural data have been sparsely...
Jul1-14 10:15 PM
Greg Bernhardt
1 2,452
Hi, I have an exercise whose solution seems too simple; please double-check my work: We have a product manifold...
Jul1-14 10:15 PM
Greg Bernhardt
1 2,536
Suppose we have a foliation of leaves (hypersurfaces) with codimension one of some Riemannian manifold ##M## with...
Jun27-14 07:56 AM
2 4,052
Suppose one has a foliation of a manifold ##M## with codimension one leaves that are all isometric. What is such a...
Jun27-14 06:35 AM
3 2,930
I'm looking to prove the Global Frobenius theorem, however in order to do so I need to prove the following lemma: ...
Jun26-14 10:37 PM
Greg Bernhardt
1 2,651
A scalar field can be the exact form of a vector field (potential form)? It's make sense?
Jun26-14 03:38 PM
7 2,861

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