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

Feb2313 09:25 AM
micromass

1 
30,178 
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 
6,803 
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 
2,845 
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 
1,371 
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 
1,647 
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 
1,651 
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 
2,416 
Can anyone tell me a good quotation about topology?

Sep2610 10:54 AM
quasar987

7 
1,526 
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 
2,294 
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 
3,473 
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 
2,008 
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 
2,308 
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 
3,027 
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 
1,687 
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 
3,773 
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 
2,672 
What are differential forms?
Is this what I'm gonna learn about in my upcoming differential geometry class?

May905 02:58 PM
mathwonk

8 
3,460 
Hello.
I was wondeirng if anyone knew any good textbooks on Differential Geometry for independent study, at an...

Sep905 12:25 AM
Tzar

8 
4,539 
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 
5,015 
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 
2,522 
Hi everybody,
How can one show that the tangent bundle TS² of the 2sphere is not trivial ? I know we can use the...

Mar309 08:32 AM
wofsy

8 
6,879 
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 
20,140 
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 
8,680 
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 
2,145 
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 
3,247 
Hello,
I am doing a project on Riemann but I don't understand some of his contributions. For instance, I do not...

Feb407 07:51 PM
mathwonk

8 
1,750 
Is it true that f is a continuous function from A \times B to C
(A, B, C are topological spaces)
if and only if...

Aug1107 10:56 AM
mathwonk

8 
2,229 
My professor recently defined immersions and embeddings in class, but he didn't really make any attempt to motivate...

Apr808 03:10 PM
wofsy

8 
2,879 
Hi, everyone:
I was just going over some work on Hyperbolic geometry, and noticed that
the geodesics in...

Dec907 04:23 PM
Chris Hillman

8 
5,768 
I need to prove that for every continuous function f:X>X of a metric and compact space X, which satisfy for each two...

Feb1608 11:30 AM
MathematicalPhysicist

8 
2,757 
I am having difficulties grasping the consequences of this theorem, would really appreciate a little enlightenment.
...

Mar1908 10:42 PM
mathwonk

8 
2,348 
I have a quetion about the forms.
When we say, "differential forms of degree one (or more)" rather than degree...

Apr908 06:26 AM
Doodle Bob

8 
2,339 
Let M be a compact manifold and C(M), C^{\infty}(M) denote rings of continuous (resp. smooth) real functions on M. Let...

May808 03:14 PM
neworder1

8 
2,122 
I'm reading this book on modern geometry and I was wondering if I'm doing these problems right:
if I'm give a...

Oct408 06:21 AM
Cexy

8 
4,724 
Hey guys,
How exactly do you take the trace of a tensor product? Do I take the trace of each tensor individually...

Nov2108 06:25 AM
tinytim

8 
6,574 
Let's take a simple example.
Both a cylinder and Möbius strip consist of a circle with a line segment associated...

Nov2308 06:49 AM
pellman

8 
2,191 
Show that any basic open set about a point on the "top edge," that is, a point of form (a, 1), where a < 1, must...

Dec808 07:42 PM
mathsss2

8 
2,627 
Hi, everyone :
I read a problem posted somewhere else on showing that, "for the correct value m
an integer"...

Mar909 01:15 AM
quasar987

8 
2,118 
We saw in the thread Definition of arc length on manifolds without parametrization that arc length that is usually...

Mar1809 03:03 AM
mma

8 
1,819 
What fields of interest in topology (or else) should I learn to fully understand his proof?
Is there a comprehensible...

Apr1409 07:10 AM
wofsy

8 
2,661 
Question: Let M, N be orientable closed nmanifolds. Knowing that the nth homology group of an orientable closed...

Apr1509 04:21 AM
Hurkyl

8 
4,457 