# Differential Geometry

- Manifolds. Tensors and forms. Connections and curvature. Differential and algebraic topology
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 Meta Thread / Thread Starter Last Post Replies Views Views: 5,318 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 31,375 what do we mean by "Finsler geometry is just Riemannian geometry without the quadratic Restriction " . i don't... Nov5-10 04:09 PM math6 2 1,032 can we define a metric on a submanifold of as follows: M is a manifold equipped with a Riemannian metric g, we denote... Nov5-10 02:29 PM math6 2 1,084 This should hopefully be a quick and easy answer. I'm running through Lee's Introduction to Smooth Manifolds to... Nov5-10 11:33 AM Kreizhn 9 1,491 I dont know if this is the right place to post this question so i'll also be posting it in the GR section, but anyway.... Nov5-10 10:22 AM vitaniarain 0 1,320 Hello I am curious about this. Uryshon' s lemma is also known as "the first non-trivial fact of point set topology",... Nov4-10 04:36 AM facenian 5 1,409 if we have a vector space V,can we define the tangent bundle of V rated TV? Nov3-10 02:47 PM math6 2 1,056 excuse me but if someone can give me the exact definition of a sub-elliptic differential operator . thnx a lot . Nov3-10 03:29 AM math6 2 814 Let's say I want to use the spherical law of cosines to determine the distance between two points. How do I calculate... Nov2-10 09:20 AM NobodySpecial 1 2,006 Is there any non-orientable one-dimensional manifold ? If not, how to prove it? Thanks! Nov2-10 07:20 AM quasar987 1 2,445 hey, i'm getting really confused with something. If i have the covariant derivative of say, constant * exp(2f), is... Nov2-10 07:19 AM arkajad 3 1,878 Hello. I was wondering if anyone here could help me understand this method I found described in the paper: "A... Nov1-10 12:34 PM Protected 0 1,944 Define 2-tori as {(z1,z2)| |z1|=c1,|z2|=c2} for c1 and c2 are constants, how to show that it is diffeomorphic to S^3 Oct31-10 09:09 PM robforsub 4 1,300 So I consider myself decently strong in algebra but many of the basic, important notions in algebraic geometry are not... Oct31-10 11:39 AM mathwonk 9 2,256 I've been looking at the Birkhoff-von Neumann polytope, and the book stated that the vertices are given by the... Oct30-10 02:18 PM mynameinc 6 1,110 hello! just a quick question, does the covariant derivative of the metric give zero even when the indices(one of the... Oct30-10 12:16 PM haushofer 3 1,363 How to find the angle of diagonal of a rectangular prism? On which plane will that be measure and why is it that so? Oct30-10 05:16 AM k.udhay 0 2,265 Hi, everyone: My prof. recently made a statement to the effect that , given a handlebody decomposition of a... Oct29-10 07:27 PM Bacle 0 684 I might have forgotten about it cause I took a similar course two years ago. So I have this assertion: Let F be a... Oct29-10 09:33 AM MathematicalPhysicist 5 1,498 Hi folks, I am following this pattern: http://www.bit-101.com/tutorials/3D-rotation.html to build a 3d model of... Oct29-10 07:59 AM ducati321 0 948 This is from O'Neil's differential geometry. I'm having trouble parsing through the problem/hint. Given any curve... Oct29-10 01:08 AM chaotixmonjuish 2 1,409 let M be a manifold and g a metric over M . is it true that every subbundle from M must have the same metric g ? Oct28-10 03:44 AM arkajad 5 1,128 I will preface this by saying that if anyone has the following book: Euclidean Geometry and Transformations written by... Oct27-10 02:17 AM tiny-tim 5 1,306 I want a projection of Earth where distances are undistorted. i.e. 10 degrees of latitude at the equator is exactly... Oct26-10 11:06 AM DaveC426913 2 1,224 Hello all, Here is my question while reading a proof. For a compact set K in a separable metrizable spce ... Oct25-10 05:02 PM Office_Shredder 5 1,298 I'm trying to create a program which will do these calculations. I am given Latitudes, Longitudes, and ellipsoidal... Oct24-10 12:22 PM G4CKT 1 1,831 Tensor densities are normally defined in terms of coordinate transformations. Could they also be defined as functions... Oct24-10 09:20 AM arkajad 14 2,698 Do you agree that the following identity is true: \int_S (\nabla_\mu X^\mu) \Omega = \int_{\partial S} X \invneg ... Oct24-10 07:06 AM arkajad 8 2,301 I get in essence what the covariant derivative is, and what it does, but im having trouble with the definition, of all... Oct24-10 02:21 AM Phrak 8 1,264 Few days back I posted a question here that dealt with inversion geometry. A point P inside a sphere can be inverted... Oct24-10 01:23 AM jasomill 1 1,673 Theorem: If a straight line intersects one of the sides of the asymptotic triangle ABOmega but does not pass through a... Oct23-10 09:05 AM ILoveJesseJam 0 2,371 Hello, not sure if this the right place or not to post this, but I am after a definitive answer to the definition of... Oct22-10 10:29 PM Moss Pauly 0 695 I'd like some help understanding three things. - What is the topology of the Grassmann manifold or oriented... Oct22-10 02:41 PM lavinia 13 2,125 Hi everyone, I've tried googling how to calculate a straight line distance on a sphere. I got no answers for it... Oct22-10 01:37 PM G4CKT 6 1,635 Hi everyone. I have been around a problem that I cannot figure out a solution (if there is one) which is related... Oct22-10 12:16 PM _Seven_ 2 2,305 Is it true that for all antisymmetric tensors F^{\mu\nu} the following identity is true: \nabla_\mu \nabla_\nu... Oct22-10 07:36 AM arkajad 4 2,127 Hi friends; can someone tell me how to prouve that the cartan tensor is defiend in SM ( the projective sphére bundle... Oct22-10 03:25 AM math6 2 972 I am writing a program that uses Snell's Law for refraction of light through two interfaces and I've encountered a... Oct21-10 10:19 PM Ralajer 0 765 Can a connected space have a countable disjoint cover of closed subsets with at least two elements? Oct21-10 04:43 PM Jamma 15 2,347 Attached are 3 of the images I created from a simple basic Moebius Band in the ChaosPro 3.3 In each one; I severed... Oct20-10 11:08 PM antarctica246 0 2,139 Here's something that's bothering me a bit. Let f : X --> Y be a continuous function, where X and Y are topological... Oct20-10 04:43 PM radou 22 2,231

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