
Please post any and all homework or other textbookstyle problems in one of the Homework & Coursework Questions...

Feb2313 09:25 AM
micromass

1 
31,092 
Just wondering if Traces can be applied to tensors.
If the Ricci tensor is Rii then is sums over diagonal elements....

Jan1110 12:02 PM
Omega137

7 
7,122 
I quote Wikipedia:
I try to apply this to the natural connection on the tangent bundle of M = S2 (or more...

Jun1510 10:15 AM
ArashYavari

7 
2,678 
What is a local invariant? For instance, at
http://en.wikipedia.org/wiki/Differential_geometry#Symplectic_geometry...

Oct1409 12:26 AM
zhentil

7 
1,644 
Any two continuous maps from X to Y, where Y is a convex subset of R^n, are homotopic. For example, the functions f(t)...

Jan1310 01:46 PM
wofsy

7 
1,951 
On page 7 it gives two conditions for a linear function on the space of pvectors built from a linear function on the...

Jan2810 06:55 AM
wofsy

7 
2,014 
Hello,
Suppose that I have a cell complex and I want to define it's geometric realization, I can do it via...

Feb1810 10:14 AM
wofsy

7 
1,697 
What kind of sets exhibit the wada property? I know R2 does but does it extend to R3 or R itself?

Feb2310 10:28 AM
tt2348

7 
1,353 
I'm sorry if this should be in the Analysis forum; I figured it pertained to topology though.
Let Y be a subspace of...

Mar210 02:43 PM
Bleys

7 
1,540 
Hi, everyone:
A couple of questions, please:
1) Examples of representative surfaces or curves:
Please...

Apr810 12:22 AM
Bacle

7 
1,042 
Hi,
Is it true to say on a topological manifold one can always find a unique metric such that a set of non...

Mar3110 02:11 AM
o_parhizkari

7 
1,383 
Let's denote the ordinary metric with d, so that d(a,b) = \sqrt{(a_1b_1)^2 + (a_2b_2)^2}, and then let e denote some...

Mar3110 05:11 PM
jostpuur

7 
2,049 
I have seen it mentioned in various places that the Lie algebra of the diffeomorphism group of a manifold M is...

May1310 02:30 PM
zhentil

7 
3,248 
How is a straight line/straight curve defined (in contexts where it is meaningful) ?
I am trying to wrap my mind...

May3110 06:35 PM
lavinia

7 
2,202 
I have been asked if the following is true or false
the intersection of two connected sets is connected ?
I...

Jun510 03:02 PM
Jamma

7 
3,049 
Hi, everyone:
I am trying to find a result for the number of bundles (up to bundle iso.) over a fixed
base...

Jun2410 08:15 AM
lavinia

7 
1,671 
Given a smooth manifold with no other structure (like a metric), one can define a derivative for a vector field called...

Jun1910 12:45 PM
quasar987

7 
1,358 
I'm reading Analysis on Manifolds by Munkres and in the section Review of Topology Munkres states the following...

Jun2510 10:37 PM
Buri

7 
3,210 
Hi i'm using Kreyszig's Introductory Functional Analysis with Applications and he proves that the set of continuous...

Jun2710 02:44 PM
Landau

7 
6,849 
Hi, Everyone:
There is an exercise in the beginning of Bott and Tu's Diff. Forms in
Algebraic Topology, of...

Sep2010 03:20 PM
mathwonk

7 
2,883 
Quick question:
Suppose I have a (transitive) R^n action on a manifold M. If the isotropy group of R^n is discrete,...

Aug3010 01:50 AM
Office_Shredder

7 
1,389 
Like the title says, what is the easiest way to see that CP^1 is topologically just a 2sphere? Wikipedia says that...

Sep710 06:39 AM
arkajad

7 
1,681 
I heard this puzzle on the MathFactor podcast (which I highly recommend).
If you don't know what Asteroids is...

Sep1810 08:20 AM
DaveC426913

7 
1,661 
What would a 3D ball look like if it were partially in 4D space when none of the 4th dimension is visible to the 3D...

Oct710 01:47 PM
Jamma

7 
2,427 
Can anyone tell me a good quotation about topology?

Sep2610 10:54 AM
quasar987

7 
1,536 
I am terribly confused on the issue of trivial tangent bundles. I understand intuitively why some tangent bundles are...

Oct510 11:51 AM
arkajad

7 
2,422 
Hi,
I know that you can determine that the Gaussian curvature of a cone tends to infinity at the vertex, but seeing...

Oct1710 02:05 PM
arkajad

7 
3,515 
OK. Suppose you have a surface with a closed curve as a boundary. Then suppose that surface grows like a soap bubble...

Apr1404 04:55 PM
selfAdjoint

8 
2,025 
On a pseudoRiemannian manifold we can contract the Riemann curvature tensor to form the Ricci tensor. In this process...

Apr1006 12:48 PM
Perturbation

8 
2,337 
Hi
we define the projectif space P^n \mathbb{R}
by the quotient space :\mathbb{R}^{n+1}/\sim where:
x\sim...

Nov1004 09:25 PM
Astronuc

8 
3,037 
Is the manifold a space defined by the metric tensor or is it a completetly different thing. I'm new to tensor...

Mar305 11:21 AM
mathwonk

8 
1,701 
Those of you who know me know that my formal education is in physics, not mathematics. So hopefully you'll excuse the...

Mar2705 05:24 PM
pmb_phy

8 
3,908 
Hello
I have a small pb:
Let \displaystyle{M=\mathbb{R^{2}\{(x,y);x=0\quad ou \quad y=1}
Let D such that ...

Apr605 08:57 PM
PBRMEASAP

8 
2,684 
What are differential forms?
Is this what I'm gonna learn about in my upcoming differential geometry class?

May905 02:58 PM
mathwonk

8 
3,538 
Hello.
I was wondeirng if anyone knew any good textbooks on Differential Geometry for independent study, at an...

Sep905 12:25 AM
Tzar

8 
4,580 
First of all, I'm not sure if this is the right forum, but none of the forums mention topology in their description. ...

Nov2805 03:54 PM
matt grime

8 
5,062 
I would welcome the parametric equations for an embedding in R3 of a locally Euclidean Möbius Strip without self...

Dec2305 12:19 PM
Ogai

8 
2,547 
I'm encountering the gradient of a vector field in a problem at the moment. Not the divergence, specifically the...

Nov1406 01:36 PM
gvk

8 
20,224 
Can anyone point me to good reference that fully develops the geometry of geodesic curvature? Most of the ones I have...

Oct206 05:17 AM
robphy

8 
8,843 
I just finished learning the fundamental theorem of curves in 3 dimensions. As a reminder, this is the theorem that...

Dec106 04:31 PM
Chris Hillman

8 
2,174 
I'm reading "tensor analysis on manifolds" by Bishop and Goldberg. I have taking a course in differential geometry i...

Nov2106 08:54 AM
mrandersdk

8 
3,275 