# Differential Geometry

- Manifolds. Tensors and forms. Connections and curvature. Differential and algebraic topology
 Meta Thread / Thread Starter Last Post Replies Views Views: 2,661 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 31,154 Hi all, does anyone know if there exists a result that proves/disproves the following?: "If a half-space \{x \in... Nov21-12 10:18 AM hwangii 0 1,016 Hi, I wish to study (non-trivial) algebraic functions which have varied cycles at a few places other than the... Nov21-12 09:17 AM jackmell 1 1,069 Hi guys, I have a very general question but I would like opinions asap. I am doing a project on Hilbert... Nov18-12 07:07 PM micromass 1 1,144 Hi, Again: I'm trying to show that, given a 3-manifold M, and a plane field ρ (i.e., a distribution on TM) on M,... Nov17-12 06:47 AM quasar987 11 1,877 Hi, All: There is a standard method to construct a nowhere-zero form to show embedded (in R^n ) manifolds are... Nov15-12 03:53 PM lavinia 8 1,308 hello, I'm trying to understand catmull-clark A. but I'm having a hard time with this... Nov13-12 06:48 AM kiyoshi7 0 995 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 1,072 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 1,667 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 2,317 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 1,061 Hi, All: I need some help with some "technology" on differential forms, please: 1)Im trying to understand... Nov12-12 07:26 AM quasar987 1 930 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 1 924 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 1,578 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 1,107 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 1,306 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 1,241 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 1,904 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 1,139 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 1,411 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 1,916 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 1 875 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 0 871 given a compact, orientable, n-dim. Riemann manifold, what is a sufficient condition for globally vanishing curvature... Oct30-12 11:36 AM lavinia 5 1,355 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 1,170 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 1,027 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 1,169 prove that for any graph G, kappa (G) ≤delta (G). Oct27-12 01:14 AM Bacle2 3 1,119 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 1,522 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 1 909 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 1,627 Hi, I've run into a problem with expanding algebraic functions via Newton polygons. Consider the function: ... Oct23-12 01:13 PM mathwonk 5 1,511 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 1 783 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 1,324 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 9,818 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 1,043 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 1,575 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 3,874 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 4 982 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 0 750 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 1,034