# Differential Geometry

- Manifolds. Tensors and forms. Connections and curvature. Differential and algebraic topology
 Meta Thread / Thread Starter Last Post Replies Views Views: 72,228 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 29,356 prove that for any graph G, kappa (G) ≤delta (G). Oct27-12 01:14 AM Bacle2 3 1,097 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 1,459 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 1 888 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 1,557 Hi, I've run into a problem with expanding algebraic functions via Newton polygons. Consider the function: ... Oct23-12 01:13 PM mathwonk 5 1,466 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 1 764 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 1,285 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 9,540 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 1,016 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 1,524 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 3,689 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 4 948 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 0 740 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 1,013 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 1,165 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 0 817 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 2,124 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 1,120 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 0 862 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 1,389 Hi, buddies, i am a mechanical engineering student, and while i was going through the concepts of Instant centers of... Oct12-12 09:37 PM anandtr2006 0 942 If I start out with a flat beam of length a and then I fix one side and then bend the other side up to form an arc... Oct12-12 06:33 PM Studiot 1 1,443 Can an ellipse's focal points be outside the ellipse? I have tried googling this, but without any good explanations or... Oct11-12 10:06 AM HallsofIvy 4 1,326 Hello there, This might be probably a simple question, but my wondering was: Is there any relation between the... Oct10-12 01:36 PM mathwonk 3 1,008 Hi all, I am trying to understand geometric flows, and in particular the Ricci flow. I understand how to calculate... Oct10-12 12:29 PM meldraft 8 1,992 I want to calculate the surface area of semi cylinder with one or both ends skew at a given angle. To calculate the... Oct10-12 12:28 AM smstoankur 3 1,521 Given a Finsler geometry (M,L,F) and $$g_{ab}^L=\frac{1}{2} \frac{\partial^2 L}{\partial y^a \partial y^b}$$... Oct8-12 05:29 AM ngkamsengpeter 0 763 I'm developing a game for the iPhone, and I have a situation where I have a graphic that the user can drag around the... Oct4-12 06:57 AM MaTHFRo 0 817 in the wikipedia page for the Levi Civita symbol, they have a definition of the product of 2 permutation symbols as: ... Oct3-12 07:34 PM demonelite123 2 3,491 \frac{}{}Hello, I've been trying to search for a general description for the Euclidean distance from a point to a... Oct3-12 05:03 PM heymaniknowyou 7 1,629 The relation between the vector operator curl and rotation in fluids and vector fields is treated thoroughly in many... Oct1-12 08:11 AM Paulibus 10 1,634 hey all, in this book ;... Sep30-12 09:05 AM zn5252 1 1,190 How do you solve ((grad(f(x,y,z))))^2? Sep29-12 08:04 PM quantumfoam 17 3,855 I'm having trouble understanding the exponential map for nonlinear vector fields. If dσ/dt=X(σ) for vector field... Sep29-12 06:39 PM quasar987 5 1,390 I posted this in yahoo questions, but perhaps this is a better place for it. The Tesseract assumes that in order to... Sep29-12 01:38 PM laserblue 14 3,155 This is really starting to bug me. I built an object out of tooth picks and glue. It's simple. An... Sep28-12 08:15 AM Alfi 1 1,210 I have two vectors: r1v=r1x*i + r1y*j + r1z*k r2v=r2x*i + r2y*j + r2z*k and r1=Math.sqrt(r1x^2 + r1y^2 +... Sep27-12 10:31 PM Muphrid 2 1,081 Here's a picture of an irregular tetrahedron, for reference: http://i.imgur.com/Y626c.png The base triangle... Sep27-12 05:42 PM torchfire 15 3,293 Hi, I have a curve defined by following parametric equation \gamma(\theta) = 1 + 0.5... Sep26-12 06:50 AM lavinia 1 879 Let $$f:U \to \mathbb{R}^3$$ be a surface with local coordinates $$f_i=\frac{\partial f}{\partial u^i}$$. Let $\omega$... Sep25-12 03:38 PM dextercioby 3 1,283