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

Feb2313 09:25 AM
micromass

1 
26,498 
I need to show that if X is Lindelof and Y is compact then XxY is Lindelof.
Now let ,XxY=U(A_\alpha x B_\beta) for...

Apr2208 01:47 PM
MathematicalPhysicist

0 
2,251 
Hi there,
I'm reading over my Lie groups notes and in them, in the introductory section on manifolds, I've written...

Apr2208 02:53 AM
mrandersdk

22 
3,933 
Im reviewing material for the exam and came across this question:
Let pi_1:RxR>R be the projection on the first...

Apr2008 05:46 PM
WWGD

3 
3,138 
Could any one help me to prove the following question:
"How can we show that the set {A in GL(n;R)  det(A)>0} is...

Apr2008 05:24 PM
WWGD

4 
2,382 
Could someone please help me with: if N,M are diffeomorphic manifolds,
what property do they share that...

Apr1508 08:07 PM
wofsy

22 
4,278 
Hi , everyone
I have a problem with geodesic equation .
I know the method of solving it , but I can't understand the...

Apr1508 05:21 PM
the shadow

14 
6,837 
I'm a bit confused as to how the text Tensor Analysis on Manifolds, by Bishop and Goldberg on page 6.
The authors...

Apr1408 04:54 PM
Doodle Bob

3 
1,994 
Does any one know why a max abliean subgroup of a compact Lie group is not necessary Max. torus? any exmaple?
Thanks!

Apr1208 01:00 PM
jojoo

0 
2,000 
Hi guys
I was first introduced to diagrammatic notation in Roger Penrose's book "Road to Reality".
I wanted to...

Apr1008 06:40 PM
shoehorn

1 
1,804 
I am trying to understand differentiable manifolds and have some questions about this topic:
We can think of a...

Apr1008 07:14 AM
wofsy

3 
2,214 
Another question:
How do we define compatibility of atlases and a maximal atlas?
why do we need to define them?...

Apr908 08:03 PM
wofsy

15 
3,263 
noob here
* indicates multiply (or 'operate on'), d_c is partial derivative w.r.t. c
tensor indices have always...

Apr908 04:20 PM
jiggers

0 
2,255 
Hi
I'm looking for a simple definition fo the affine connection because I can't understand it's meanning , that...

Apr908 01:55 PM
LorenzoMath

12 
6,671 
Affine spaces can be regarded as smooth manifolds if we take the natural topology and affine coordinate charts as...

Apr908 07:51 AM
wofsy

9 
2,947 
Hi everyone,
I've been studying on Gauss map for while. I have a question about the isotropy subgroup. I know its...

Apr908 07:03 AM
saddy

0 
1,418 
Hi everyone,
I've been studying on Gauss map for while. I have a question about the isotropy subgroup. I know its...

Apr908 06:41 AM
saddy

0 
2,042 
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 
2,244 
My assignment is to prove that the next groups: SO(n),U(n),SL(n,R) are path connected, and that the groups...

Apr808 09:51 PM
wofsy

10 
4,701 
Hello.
Suppose that \sigma: (M, g) \to (N, h) is an isometric diffeomorphism between two Riemannian manifolds M and...

Apr808 09:19 PM
wofsy

4 
1,697 
The product of the principal curvatures of a surface in Euclidean 3 space, though defined extrinsically, is actually...

Apr808 08:44 PM
wofsy

5 
1,718 
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 
2,785 
In calculus on manifolds, within one of the problems of this book the dual space is indirectly defined. I'll quote:
...

Apr808 08:12 AM
wofsy

9 
2,554 
I'm taking a class in differential geometry in the fall and I wanted to be sure to be well prepared. Are there any...

Apr708 09:52 PM
hanskuo

22 
3,431 
Is it possible to have a tangent vector field on the unit 2sphere x^2+y^2+z^2 =1 in
3D which vanishes at exactly one...

Apr708 09:19 PM
wofsy

6 
5,077 
A hypersurface of Euclidean space inherits a Riemannian connection by tangential projection of the flat Euclidean...

Apr708 07:29 PM
wofsy

0 
1,061 
Does anyone know what the Dirac delta function would look like in a space with curvature and torsion? The Dirac delta...

Apr708 12:03 PM
friend

6 
2,795 
Hello all.
In a quite easy to follow short piece by Edmond Bertschinger entitled Introductio to Tensor Calculus for...

Mar2708 06:40 PM
matheinste

4 
9,997 
Hi, everyone:
I apologize if this is out of place. Please let me know if so, and
feel free to remove.
I am...

Mar2708 02:27 PM
WWGD

10 
2,109 
My differential forms book (Flanders/Dover) defines an inner product on wedge products for vectors that have a defined...

Mar2708 11:13 AM
Peeter

6 
4,673 
Hello,
One says that an odd derivation d is a differential modulo another differential d' if this two things hold:...

Mar2308 12:34 AM
astros

2 
1,494 
This semester i'm taking "Introduction to Algebraic Curves" course. Up to now, the only problems i have with this...

Mar2208 10:17 AM
sylar

0 
2,209 
I am having difficulties grasping the consequences of this theorem, would really appreciate a little enlightenment.
...

Mar1908 10:42 PM
mathwonk

8 
2,281 
Hi, everyone
I have studied on a problem for a while on Lie algebras and manifolds. Unfortunately I know very little...

Mar1808 09:18 AM
saddy

0 
1,783 
I need to show a particular map f:M>N is an isometry (globally). M,N are riemannian manifolds, p is a point on M....

Mar1608 10:34 PM
Cincinnatus

4 
6,545 
I have a question about Lie subalgebra.
They say "a Lie subalgebra is a much more CONSTRAINED structure than a...

Mar1608 09:53 PM
KarateMan

5 
1,655 
Can someone explain to me how to go from
\Gamma ^k_{ij}=\bold{e}_j \cdot D_i \bold{e}^k
To
D_i \bold{e}^k =...

Mar1608 08:32 PM
hanskuo

2 
1,423 
Hi, everyone:
I am doing some reading on the Frolicher Spec Seq. and I am trying to
understand better the...

Mar1008 01:15 AM
WWGD

5 
2,063 
Usually the adjoint to the exterior derivative d^* on a Riemannian manifold is derived using the inner product ...

Mar908 07:51 PM
HenryGomes

5 
3,766 
I have a few questions on this topic, and i want to see if i got them partially right or wrong.
1.\pi_1(X,x_0) is the...

Mar808 11:01 AM
MathematicalPhysicist

7 
1,789 
If we have as a manifold euclidian R^2 but expressed in polar coordinates...
Do any circle centered at the origin...

Mar608 09:32 AM
HallsofIvy

7 
3,975 