Differential Geometry

- Manifolds. Tensors and forms. Connections and curvature. Differential and algebraic topology
 Meta Thread / Thread Starter Last Post Replies Views 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 26,438 let x a point on complex manifold X, z_j a coordinate system at x , E a holomorphic bundle and let h_α be a... Sep11-12 11:39 AM math6 0 769 Hello, the definition of diffeomorphism is: a bijection f:M\rightarrow N between two manifolds, such that both f and... Sep9-12 02:22 AM mnb96 7 1,183 I am a physicist trying to understand the notion of holonomy in principal bundles. I am reading about the... Sep8-12 03:49 PM lavinia 3 1,822 Just like the title says, what is a dual vector. I am reviewing Panton's "Incompressible Flow", Chapter 3, and a brief... Sep7-12 11:39 PM homeomorphic 9 2,151 Hello all, this is my first topic here at PF, though I have been using this site as a homework aid for quite a while.... Sep3-12 08:21 PM GPundergrad 6 2,329 Hello, So, given two points, x and x', in a Lorentzian manifold (although I think it's the same for a Riemannian... Aug30-12 05:27 PM TrickyDicky 7 2,715 hello! i'm new over here.. Hope i'm writing where it should be written. What is the solution of ... Aug30-12 05:12 PM Mute 5 2,215 Say we take N random points in a volume V and connect the points pairwise with line-segments. I would like to estimate... Aug29-12 08:31 PM Spinnor 2 1,308 Here is the problem: If M is a manifold with boundary, then find a retraction r:U→∂M where U is a neighborhood of ∂M.... Aug29-12 08:15 PM xaos 2 910 Hey folks, Bit of a complex question here, but I'm hoping someone smarter than myself can help me figure this out. I... Aug29-12 04:18 PM AtlasSniperma 2 1,143 Would someone here be able to write down for me an example of a metric on a manifold with both macroscopic dimensions,... Aug29-12 10:30 AM HallsofIvy 3 934 Given a real vector space, I understand the significance of defining a complex structure. Now, if J is a complex... Aug28-12 10:38 PM chiro 1 928 I'm having difficulty understanding the nature of a plane in complex space. Specifically, I have two complex (N... Aug28-12 05:42 PM christoff 25 2,749 A 180 degree circular arc (i.e. a half sphere) is obvious: http://i.imgur.com/Upx2A.png When you rotate this... Aug26-12 12:12 AM murrdpirate0 2 1,517 :cry::cry::cry::cry::cry::cry::cry::cry::cry::cry::cry::cry::cry::cry::cry::cry::cry::cry::cry::cry::cry::cry::cry::cry... Aug26-12 12:07 AM jedishrfu 2 1,114 According to the link below, fractal dimension is an exponent of some sort:... Aug25-12 07:42 AM HallsofIvy 1 1,072 Hello! Could anybody give me some hint with the following problem? Consider a smooth, compact embedded submanifold M =... Aug24-12 05:05 PM Goklayeh 1 842 I have a regular curve, \underline{a}(s), in ℝN (parameterised by its arc length, s). To a running point on the... Aug23-12 03:05 PM weetabixharry 7 1,473 Exercise #27 from a textbook called Kiselev's Geometry / Book I. Planimetry: Using only compass, construct a 1... Aug23-12 06:31 AM coolul007 2 1,579 A book I'm reading (Companion to Concrete Math Vol. I by Melzak) mentions, "...any ellipse occurs as a plane section... Aug22-12 05:04 PM imurme8 2 953 Consider a circle of diameter d. Inscribe a triangle within the circle so that the triangle has hypotenuse d. ... Aug22-12 02:43 PM zoobyshoe 8 1,183 I have recently experimented with algorithms for rendering colour gradients. Linear gradients are no problem, but... Aug21-12 12:18 AM Ostsol 1 1,146 Not sure if this is a topology question but here goes. Imagine an infinitely long piece of string and I cut it in... Aug20-12 07:25 PM QuantumHop 10 1,489 I can figure out how to do a rigid rotation in n dimensions. Next I want to look at non-rigid rotations. Lets... Aug19-12 07:20 AM lavinia 4 1,123 I read some books and see that the definition of covariant tensor and contravariant tensor. Covariant tensor(rank 2)... Aug17-12 02:20 PM StationZero 3 11,067 In a game I'm developing, I have an ellipse which contains a blue shape inside of it like follows: ... Aug16-12 07:25 PM chiro 3 1,109 If we want to solve $$f(x)=0$$ we can re-write the equation as $$g(x)=x$$ and use the fixed point method, i.e,... Aug15-12 02:02 PM Charles49 3 1,195 Knowing the initial point of a vector (X1,Y1) and its magnitude and angle (R,θ) HOW CAN I CALCULATE ITS FINAL POINT... Aug12-12 08:53 AM Studiot 7 2,234 If we have a unit circle within a square s.t. the square touches the circle in 4 places then the biggest gap we can... Aug11-12 07:01 AM HallsofIvy 11 1,844 Hello, let's suppose I have the following system of curvilinear coordinates in ℝ2: x(u,v) = u y(u,v) = v + e^u where... Aug9-12 11:00 AM mnb96 0 794 Hello, Can anyone explain to me, or tell me a good source where I can find the divergence theorem in a Lorentzian... Aug8-12 06:21 AM PLuz 0 884 hi friends, Suppose we have a vector bundle E equipped with a hermitian metric h, and in a subbundle of E noted SE .... Aug7-12 07:57 PM Ben Niehoff 1 950 How can I calculate degrees of freedom of a rank (o,3) tensor, Aabc, that is mixed symmetry and antisymmetric in the... Aug7-12 03:37 PM sourena 3 1,213 Hello all, this is my first time posting on this forum, so to start with, it's good to meet you all and thanks in... Aug5-12 09:36 PM EuphoGuy 0 804 Suppose I have a vector space. There is circle with center at the origin of the vector space. There is also a line L... Aug5-12 05:08 PM meldraft 3 1,732 This about those magnetic toys buckyballs. My apologies, I don't really know any physics, so sorry if my terminology... Aug4-12 04:33 AM ImaLooser 1 1,114 Consider the unit ball B:=B_1(0)\subset \mathbb{R}^2. How can one prove that the set B\times B \setminus D, where... Aug1-12 08:34 PM lavinia 2 931 Ok, so I'm trying to plot the unit circle using the chebyvhev metric, which should give me a square. I am trying this... Aug1-12 10:14 AM meldraft 0 1,150 A math question about projections of lines: Say we have two straight lines which we consider as number lines... Jul31-12 07:28 PM imurme8 0 785 Not much. Im not sure where to put this so mods move it as need Anyways here is the back story, We have been... Jul31-12 12:31 AM chiro 3 1,165