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Differential Geometry

- Manifolds. Tensors and forms. Connections and curvature. Differential and algebraic topology
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Please post any and all homework or other textbook-style problems in one of the Homework & Coursework Questions...
Feb23-13 09:25 AM
1 26,504
Given a smooth vector field ##V## on a smooth manifold ##M## the uniqueness of differential equations assures that...
Jan25-14 10:07 AM
1 542
I have some important questions and essentials for understand some theories. They are six: given f(r(t)), f(r(u, v)),...
Jan24-14 07:19 AM
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##...
Jan24-14 05:26 AM
1 505
Hello, I was wondering the following. Suppose you start with a Riemannian manifold M. Say you know one geodesic....
Jan22-14 08:57 PM
2 545
Is possible to write an unit vector in its differential form, like:...
Jan22-14 01:47 PM
0 510
Hi, all: I'm trying to understand the meaning of the term "null-homotopic framing". Say K is a knot embedded in...
Jan21-14 11:09 PM
0 499
I was wondering what it would mean geometrically for a manifold to have identical components in its metric and...
Jan19-14 06:14 PM
0 524
Recently I've been studying about orthogonal coordinate systems and vector operations in different coordinate...
Jan18-14 09:36 PM
9 869
Suppose we have some two-dimensional Riemannian manifold ##M^2## with a metric tensor ##g##. Initially it is always...
Jan17-14 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...
Jan16-14 02:52 PM
William Nelso
0 537
Suppose we have a pseudo-riemannian 4 manifold S (sometimes also called a Minkowskian manifold) that is without...
Jan15-14 04:19 PM
3 583
Hi, I'm trying to show that if ## M^n ## is orientable and connected, with boundary (say with just one boundary...
Jan14-14 10:40 PM
8 700
By the well-known Whitney embedding theorem, any manifold can be embedded in \mathbb R^n. You might have also heard...
Jan14-14 08:36 PM
7 629
Hi, hope this is not too simple: Are ##S^1 ## -knots (meaning homeomorphisms of ##S^1 ## into ## R^3## or ## S^3##...
Jan14-14 05:50 PM
30 1,461
I'm a high school physics teacher trying to get a handle on differential geometry so please make explanations as...
Jan14-14 02:52 PM
1 684
From a topological point of view a homeomphism is the best notion of equality between topological spaces. I.e....
Jan11-14 09:57 AM
11 943
This is an expression I came across in a paper I am going through. It involves an expression for the parallel...
Jan10-14 04:54 AM
0 545
Think for example of the torus as a square with the proper edges identified. Viewed like this (i.e. using the flat...
Jan8-14 08:40 PM
23 1,645
In my Riemannian geometry class my teacher wrote i-vector when he was referring to the tangent vector \partial_i of...
Jan8-14 01:59 PM
0 507
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...
Jan6-14 09:08 PM
1 533
Hi, All: Let X be a Reeb vector field, and let ω be a 1-form dual to X. Is ω necessarily a contact form? I know...
Jan4-14 10:39 PM
9 662
If exist a formula for calculate the area of a closed curve:...
Dec30-13 03:44 PM
5 785
Hi, All: Sorry for the length of the post, but I think it is necessary to set things up so that the post is...
Dec28-13 01:22 AM
0 646
What's the difference between Euclidean and Riemann space? As far as I know ##\mathbb{R}^n## is Euclidean space.
Dec27-13 03:18 AM
6 831
Hi, can someone help in re-parameterizing the curve δ(t)=(2/3(√(L^2+9))cos(t),1/3(√(L^2+9))sin(t),L) I found...
Dec26-13 10:23 AM
1 1,328
Hello, I came across an argument for the fact that the degree of the map R_n which reflects the n-sphere through a...
Dec25-13 10:49 AM
4 769
Hellow!!! I known an infinitesimal relation between the solid angle Ω with the azimutal angle θ and zenital φ,...
Dec23-13 08:00 AM
2 684
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...
Dec21-13 05:21 AM
1 790
I would like to know how to divide a sphere's volume equally into 3 parts, by using two "slices" that are parallel...
Dec19-13 07:28 PM
Simon Bridge
4 849
I think you know definition of line infinitesimal: ^2 = \begin{bmatrix} dx & dy & dz \end{bmatrix} \begin{bmatrix} 1...
Dec16-13 07:09 PM
1 733
I have read statements like "assume that there exists a killingvector ##\xi## that makes it possible to compactify the...
Dec15-13 01:26 PM
center o bass
8 1,774
So, by accident, while deriving the induced metric for a sphere in 3 dimensions I realized that the transpose of the...
Dec13-13 10:49 PM
6 971
Sorry if this question seems too trivial for this forum. A grad student at my university told me that a compact...
Dec10-13 10:09 AM
2 861
Hi. I studied calculus a while back but am far from a math god. I have been reading around online about hyperbolic...
Dec9-13 11:48 AM
2 925
hi all! I have a problem related with some data analysis. I have two functions, expressin the energy resolution of...
Dec8-13 07:57 AM
0 740
Is there a rigorous integral definition of the exterior derivative analogous to the way the gradient, divergence &...
Dec7-13 09:37 PM
3 983
Hello, if we consider a diffeomorphism f:M-->N between two manifolds, we can easily obtain a basis for the tangent...
Dec7-13 05:37 AM
0 687
How do I visualize \dfrac{xdy-ydx}{x^2+y^2}? In other words, if I visualize a differential forms in terms of...
Dec7-13 04:06 AM
0 670
In Theodore Frankel's book, "The Geometry of Physics", he observes at page 248 that the covariant derivative of a...
Dec1-13 02:59 PM
center o bass
0 830
I wonder if one should study books like Gauss's General Investigations on Curved Surfaces or Euler's works or there...
Nov30-13 02:24 PM
1 915

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