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

Feb2313 09:25 AM
micromass

1 
26,479 
Given a smooth vector field ##V## on a smooth manifold ##M## the uniqueness of differential equations assures
that...

Jan2514 10:07 AM
jgens

1 
540 
I have some important questions and essentials for understand some theories. They are six:
given f(r(t)), f(r(u, v)),...

Jan2414 07:19 AM
Jhenrique

2 
552 
Let ##M## and ##N## be smooth manifolds and let ##F:M \to N## be a smooth map. Iff ##(U,\phi)## is a chart on ##M##...

Jan2414 05:26 AM
Mandelbroth

1 
505 
Hello, I was wondering the following.
Suppose you start with a Riemannian manifold M. Say you know one geodesic....

Jan2214 08:57 PM
jcsd

2 
545 
Is possible to write an unit vector in its differential form, like:...

Jan2214 01:47 PM
Jhenrique

0 
509 
Hi, all:
I'm trying to understand the meaning of the term "nullhomotopic framing".
Say K is a knot embedded in...

Jan2114 11:09 PM
WWGD

0 
499 
I was wondering what it would mean geometrically for a manifold to have identical components in its metric and...

Jan1914 06:14 PM
TrickyDicky

0 
523 
Recently I've been studying about orthogonal coordinate systems and vector operations in different coordinate...

Jan1814 09:36 PM
Chestermiller

9 
867 
Suppose we have some twodimensional Riemannian manifold ##M^2## with a metric tensor ##g##. Initially it is always...

Jan1714 09:01 AM
center o bass

6 
603 
Question, within the conformal group of say standard euclidean space can the inversion be obtained by exponentiating...

Jan1614 02:52 PM
William Nelso

0 
537 
Suppose we have a pseudoriemannian 4 manifold S (sometimes also called a Minkowskian manifold) that is without...

Jan1514 04:19 PM
PAllen

3 
583 
Hi, I'm trying to show that if ## M^n ## is orientable and connected, with boundary (say with just one boundary...

Jan1414 10:40 PM
lavinia

8 
698 
By the wellknown Whitney embedding theorem, any manifold can be embedded in \mathbb R^n.
You might have also heard...

Jan1414 08:36 PM
jgens

7 
629 
Hi, hope this is not too simple:
Are ##S^1 ## knots (meaning homeomorphisms of ##S^1 ## into ## R^3## or ## S^3##...

Jan1414 05:50 PM
jgens

30 
1,460 
I'm a high school physics teacher trying to get a handle on differential geometry so please make explanations as...

Jan1414 02:52 PM
WWGD

1 
680 
From a topological point of view a homeomphism is the best notion of equality between topological spaces. I.e....

Jan1114 09:57 AM
lavinia

11 
941 
This is an expression I came across in a paper I am going through. It involves an expression for the parallel...

Jan1014 04:54 AM
paluskar

0 
545 
Think for example of the torus as a square with the proper edges identified. Viewed like this (i.e. using the flat...

Jan814 08:40 PM
WannabeNewton

23 
1,639 
In my Riemannian geometry class my teacher wrote ivector when he was referring to the tangent vector \partial_i of...

Jan814 01:59 PM
PLuz

0 
506 
Hi, All:
Say S is a submanifold of an ambient, oriented manifold M; M is embedded in some R^k;
let ## w_m ## be an...

Jan614 09:08 PM
lavinia

1 
533 
Hi, All:
Let X be a Reeb vector field, and let ω be a 1form dual to X. Is ω necessarily a contact form?
I know...

Jan414 10:39 PM
WWGD

9 
662 
If exist a formula for calculate the area of a closed curve:...

Dec3013 03:44 PM
Jhenrique

5 
784 
Hi, All:
Sorry for the length of the post, but I think it is necessary to set things up so that the post is...

Dec2813 01:22 AM
WWGD

0 
646 
What's the difference between Euclidean and Riemann space? As far as I know ##\mathbb{R}^n## is Euclidean space.

Dec2713 03:18 AM
jgens

6 
831 
Hi,
can someone help in reparameterizing the curve
δ(t)=(2/3(√(L^2+9))cos(t),1/3(√(L^2+9))sin(t),L)
I found...

Dec2613 10:23 AM
hoops

1 
1,327 
Hello,
I came across an argument for the fact that the degree of the map R_n which reflects the nsphere through a...

Dec2513 10:49 AM
nonequilibrium

4 
768 
Hellow!!!
I known an infinitesimal relation between the solid angle Î© with the azimutal angle Î¸ and zenital Ï†,...

Dec2313 08:00 AM
Jhenrique

2 
682 
Hi so I was just wondering if the metric g=diag(e^{iat},e^{ibx},e^{icy}) (where a,b,c are free parameters and t,x,y...

Dec2113 05:21 AM
ChrisVer

1 
789 
I would like to know how to divide a sphere's volume equally into 3 parts, by using two "slices" that are parallel...

Dec1913 07:28 PM
Simon Bridge

4 
848 
I think you know definition of line infinitesimal:
^2 = \begin{bmatrix} dx & dy & dz \end{bmatrix} \begin{bmatrix} 1...

Dec1613 07:09 PM
ChrisVer

1 
731 
I have read statements like "assume that there exists a killingvector ##\xi## that makes it possible to compactify the...

Dec1513 01:26 PM
center o bass

8 
1,773 
So, by accident, while deriving the induced metric for a sphere in 3 dimensions I realized that the transpose of the...

Dec1313 10:49 PM
pdxautodidact

6 
970 
Sorry if this question seems too trivial for this forum.
A grad student at my university told me that a compact...

Dec1013 10:09 AM
Sajet

2 
860 
Hi.
I studied calculus a while back but am far from a math god. I have been reading around online about hyperbolic...

Dec913 11:48 AM
Reuel

2 
924 
hi all!
I have a problem related with some data analysis.
I have two functions, expressin the energy resolution of...

Dec813 07:57 AM
1Keenan

0 
740 
Is there a rigorous integral definition of the exterior derivative analogous to the way the gradient, divergence &...

Dec713 09:37 PM
Mandelbroth

3 
982 
Hello,
if we consider a diffeomorphism f:M>N between two manifolds, we can easily obtain a basis for the tangent...

Dec713 05:37 AM
mnb96

0 
684 
How do I visualize \dfrac{xdyydx}{x^2+y^2}?
In other words, if I visualize a differential forms in terms of...

Dec713 04:06 AM
bolbteppa

0 
669 
In Theodore Frankel's book, "The Geometry of Physics", he observes at page 248 that the covariant derivative of a...

Dec113 02:59 PM
center o bass

0 
827 
I wonder if one should study books like Gauss's General Investigations on Curved Surfaces or Euler's works or there...

Nov3013 02:24 PM
mathwonk

1 
912 