# Differential Geometry

- Manifolds. Tensors and forms. Connections and curvature. Differential and algebraic topology
 Meta Thread / Thread Starter Last Post Replies Views Views: 500 Announcement: Follow us on social media and spread the word about PF! Jan16-12 Please post any and all homework or other textbook-style problems in one of the Homework & Coursework Questions... Feb23-13 09:25 AM micromass 1 30,976 I've been thinking of a solution, but can't find a one. You have a square of side length 1. You have to draw 2 circles... Nov12-12 05:40 PM Studiot 2 1,066 Hello! I am a bit confused about how I can use covector fields on a differentiable manifold. John M. Lee writes... Nov12-12 10:10 AM Vargo 6 1,659 Hello, can anyone suggest a geometric interpretation of the metric tensor? I am also interested to know how we could... Nov12-12 09:17 AM lavinia 12 2,283 Suppose that points x and y are given in Euclidean space. Point x is displaced to point x1 by x1=x+a(x-y) Given... Nov12-12 07:27 AM tiny-tim 3 1,052 Hi, All: I need some help with some "technology" on differential forms, please: 1)Im trying to understand... Nov12-12 07:26 AM quasar987 1 925 Hello everyone, I'm studying basic graph theory, and my instructor gives me these statements to translate into... Nov11-12 07:35 PM Simon Bridge 1 922 Say I have a function F(x,y)=(f(x),g(y)), F:X×Y→X'×Y'. Is there a theorem that says if f:X→X' and g:Y→Y' are... Nov9-12 04:15 PM sammycaps 10 1,561 I am currently reading a paper discussing the convexity of the image of moment maps for loop groups. In particular, if... Nov9-12 02:32 PM Vargo 3 1,101 So I'm having a little trouble with the part of Van Kampen's theorem my professor presented to us. He called this the... Nov9-12 08:36 AM sammycaps 4 1,300 If the hyperbolic paraboloid z=(x/a)^2 - (y/b)^2 is rotated by an angle of π/4 in the +z direction (according to... Nov8-12 11:45 AM BrainHurts 2 1,223 I know that physically, they describe relationships whereby, for instance a vector field, for each point in three... Nov6-12 03:58 PM djpailo 5 1,874 Does anyone have a good book or reference on computing riemannian connections. I'm looking at Do Carmo and can't find... Nov6-12 03:49 PM lavinia 2 1,128 Let S1*(S2*) be the polar cone of the set S1(S2) (http://en.wikipedia.org/wiki/Dual_cone_and_polar_cone). How can I... Nov4-12 06:14 PM avilaca 5 1,403 Hello! I seem to have a problem with spherical coordinates (they don't like me sadly) and I will try to explain it... Nov3-12 10:00 PM chiro 3 1,901 When given a cylinder with radius, height and thickness, how does one go about computing the amount of material used... Oct30-12 09:22 PM Vargo 1 864 All, I am trying to determine the length of line across 3 dimensions (XYZ). My X&Y are WGS 84 coordinates and my Z... Oct30-12 03:43 PM entombedtrade 0 865 given a compact, orientable, n-dim. Riemann manifold, what is a sufficient condition for globally vanishing curvature... Oct30-12 11:36 AM lavinia 5 1,340 Suppose a set of k arbitrary points, x_i, 1<=i<=k, x_i from R^2 are selected from a line. How can it be shown that a... Oct29-12 11:34 AM Vargo 6 1,165 Find the vertices of α(t) = 1 - 2 cos(t) I know that to find the vertices we have to set the curvature equal to... Oct29-12 08:02 AM lavinia 2 1,020 Hi Given is a triangle on points x,y,z in the plane. This triangle has two points a and b on opposite sides (see... Oct27-12 02:00 AM chiro 7 1,164 prove that for any graph G, kappa (G) ≤delta (G). Oct27-12 01:14 AM Bacle2 3 1,112 Can someone please confirm that there is a typo in Nakahara's Geometry, Topology, and Physics, on page 319 (the last... Oct26-12 12:15 PM mathwonk 3 1,506 I shall use Seidel's definition of a Liouville domain; in particular, a Liouville domain is a compact manifold M ... Oct24-12 06:34 AM quasar987 1 904 Does anyone know where I can find an algorithm for the points of intersection of two ellipses existing with arbitrary... Oct23-12 09:34 PM Norwegian 1 1,608 Hi, I've run into a problem with expanding algebraic functions via Newton polygons. Consider the function: ... Oct23-12 01:13 PM mathwonk 5 1,501 Hello, I've just started learning about asymptotes in school. The questions I have are: 1. To find the vertical... Oct22-12 10:51 AM mathwonk 1 778 I was working on some algebraic topology matters, thinkgs like the connected sum of some surfaces is some other... Oct21-12 12:37 AM julypraise 5 1,304 I had doubts whether to post this here or in in the physics section but I did here because I'm more interested in a... Oct20-12 02:56 PM Muphrid 91 9,730 Let $$M$$ be a surface with Riemannian metric $$g$$. Recall that an orthonormal framing of $$M$$ is an ordered pair of... Oct20-12 07:24 AM Bacle2 2 1,036 Hi, You guys know of any (software) function which accepts as input an aribtrary algebraic function, then computes... Oct18-12 07:53 PM mathwonk 6 1,560 How do you calculate the Normal vector to an Ellipse. Radius Vector: r=rx*i + ry*j + rz*k Velocity Vector:... Oct18-12 04:48 PM Philosophaie 15 3,830 Let $$(M,g)$$ be an oriented Remannian surface. Then globally $$(M,g)$$ has a canonical area-2 form $$\mathrm{d}M$$... Oct18-12 08:34 AM quasar987 4 976 Let $$f:U \to \mathbb{R}^3$$ be a surface, where $$U=\{(u^1,u^2)\in \mathbb{R}^2:|u^1|<3, |u^2|<3\}.$$ Consider the... Oct18-12 03:34 AM semigroups 0 747 Hi, I need to do this for some homework and I don't really understand... could anyone help with the following... Oct17-12 11:14 PM coalquay404 1 1,027 I'm trying to write an algorithm that will create the smallest possible ellipse to encompass any number of points on... Oct17-12 11:40 AM Physt 4 1,188 Take for example, the function: a_0(z)+a_1(z)w+a_2(z)w^2+a_3(z) w^3+a_4(z)w^4+a_5(z)w^5=0 with the degree of ... Oct17-12 06:28 AM jackmell 0 851 I am having trouble getting a set definition of what constitutes a manifold for example , I have the real plane... Oct15-12 11:59 PM Bacle2 24 2,148 I got these people trying to say that you can orientate a solid oblong so that it looks half the length and width with... Oct15-12 10:34 PM Simon Bridge 3 1,147 Suppose I'm given a random function: (-8+5 z+4 z^2)\text{}+(7 z+6 z^4-7 z^5)w+(3 z^2-z^3)w^2+(-8 z-2 z^4-2... Oct15-12 08:18 AM jackmell 0 875 I'm not sure if this is the right forum. I'm actually trying to solve this for a computer program given shape A... Oct13-12 10:10 PM Muphrid 1 1,449