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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
Hi everyone, I know that there is a result that corresponding to a closed p-form α, I can find a p-1 form β, such...
Apr12-12 12:37 PM
Ben Niehoff
2 1,338
Hello, I am reading the paper of S. Ishihara, Quaternion Kaehlerian manifolds, I need it for understanding of totally...
Apr12-12 02:02 AM
0 911
Recently I have been working through a text on Differential Topology and have come across the notion of smooth...
Apr11-12 07:24 PM
1 1,236
First, I apologize for any awkward language--I'm still relatively new to mathematics. This problem seems to be related...
Apr11-12 04:18 PM
8 1,320
I'm afraid I need help again... First, these two things are shown: 1) Let v \in T_{\bar p}\mathbb{CP}^n, ||v|| =...
Apr11-12 03:52 PM
6 1,476
Can the covariant components of a vector, v, be thought of as v multiplied by a matrix of linearly independent vectors...
Apr11-12 07:53 AM
3 1,055
Dear Folks: In most textbooks on differential geometry, the regular theorem states for manifolds without...
Apr11-12 06:11 AM
1 1,320
Hey all, I have a vector field described by a complex potential function (so I have potential lines and...
Apr10-12 08:01 PM
4 1,508
Hi all! I have a discrete 2D vector field with a particular characteristic: At every point, instead of having a...
Apr10-12 12:13 AM
1 1,128
I want to show that ∇2ϕ=ρ/2, which governs gravity in Newtonian physics? I found solution of this question in ....
Apr9-12 02:41 PM
3 1,509
Dear there, A plywood sheet can bend by certain degree before it breaks. Suppose f(x,y) describes the bended...
Apr9-12 02:12 PM
0 952
Dear Folks: Here is the problem: in |z|<1, we difine a distance between any two points z1 and z2 by d(z1 , z2)...
Apr9-12 12:12 PM
Fangyang Tian
0 1,045
Dear Folks: I come across the word "cusp" in two different fields and I think they are related. Could anyone...
Apr9-12 11:22 AM
1 1,109
Dear Folks: It is well known that the preimage of a regular point is a imbedding submanifold, but is it...
Apr9-12 11:10 AM
2 1,335
What's it called when a 3D shape can be made of 2D surfaces of all the same shape and dimensions? To make a cube, I...
Apr9-12 04:01 AM
Fangyang Tian
3 2,270
Hello! I've read some lie algebra in both group theory books and differential geometry books, and is confused about...
Apr8-12 11:36 PM
Fangyang Tian
10 1,958
Hi! I'm working through this script and I'm not sure if if there is a mistake at one point, or if I'm just thinking...
Apr8-12 09:57 PM
6 1,233
I came across the following statement in this often-referenced paper on Einstein-Cartan theory (3rd page, right-hand...
Apr8-12 06:02 PM
3 1,266
Hi, I have some more questions about this stuff, which, as always, confuses me. I am (extremely slowly) working...
Apr7-12 11:14 PM
2 1,537
Dear Folks: Is there any relation between Curvature Operator and Universal Eveloping Algebra, since they look...
Apr7-12 11:36 AM
Fangyang Tian
0 972
i see the definition of differential manifolds in some book for example, NAKAHARA but what is the definition of...
Apr6-12 02:05 AM
4 1,285
Problem: In circle C chords AB and XY intersect at P. Prove that the projections of P onto AX, BX, AY , BY are...
Apr5-12 10:38 PM
0 1,010
consider we have a map. what condition should have our map that it has inverse?
Apr4-12 11:39 PM
2 1,236
Hello. I have a question that has been on my mind for some time. I always see in mathematical physics books that they...
Apr4-12 11:53 AM
9 2,088
Hi! I'm trying to work through a script on Riemannian submersions but I have some problems with one proof in...
Apr3-12 07:28 PM
7 1,225
Hi, All: It's been a long time since I did this, and I have some basic doubts; please bear with me: In Lee's...
Apr2-12 06:04 PM
4 1,711
From the things I've read on manifold geometry,metric is a property of the manifold.Maybe you can call it intrinsic....
Apr2-12 05:05 PM
12 1,818
Hi, I'm looking for software that allows me to manipulate tensors as symbols themselves, i.e. not as lists of...
Apr2-12 02:37 PM
0 1,284
I am reading through Kiselev's Geometry: Book I. It is a plane geometry textbook and in the introduction it says the...
Apr2-12 12:40 PM
8 1,895
Simple question I am confused on. If I have a tensor M^{\alpha\beta\gamma} that is totally antisymmetric in its...
Apr1-12 09:41 AM
3 1,566
Hello, I am currently going over Nakahara's Geometry, Topology, and Physics and even though I have bumped into some...
Mar31-12 12:33 PM
5 1,960
I've been thinking about complex residues and how they relate to the topology of a function's Riemann's surface. My...
Mar30-12 02:16 PM
1 1,275
How many ways in the entire world are there for computing Puiseux expansions of algebraic functions? I know of three...
Mar29-12 06:29 AM
2 1,488
I want to prove the next assertion in Jeffrey M. Lee's Manifolds and differential geometry. If \mathcal{D}_1,...
Mar29-12 01:02 AM
1 1,050
Folks, I am looking at my notes. Wondering where the highlighted comes from. Prove that a finite orthogonal set is...
Mar28-12 01:28 PM
3 1,397
I need to prove that every line is contained by at least two planes using only the incidence axioms. This is what I...
Mar28-12 12:33 PM
2 1,152
I need to prove the interior of <ABC is a convex set. I know it is. I started by defining the angle as the...
Mar28-12 12:30 PM
3 1,518
If torsion = anti-symmetric part of the connection coefficients, and ...
Mar27-12 06:50 PM
8 2,505
The following is a problem that I’m sure is considered “basic” for mathematicians. I would therefore be gracious if...
Mar27-12 01:42 PM
2 1,417
The following is a distance formula for a metric/pseudometric space. Please. Can anyone give me ANY insight...
Mar26-12 07:38 PM
0 1,182

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