# Differential Geometry

- Manifolds. Tensors and forms. Connections and curvature. Differential and algebraic topology
 Meta Thread / Thread Starter Last Post Replies Views Views: 4,742 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 31,350 The exterior derivitive 'd' ( 1 2 3 ... Last) I am attempting to teach myself differential geometry (being bereft of creditied educational institutions in my area)... Nov7-06 01:41 PM quetzalcoatl9 89 9,665 This is an example from Bott and Tu 's book DFAT(page 125).The example is in the image.I don't understand why can we... Nov22-11 08:49 PM lavinia 3 1,585 Could someone shortly summarise the essence of Stone's theorem ? What is the difference between Stone's theorem and... Jun16-13 04:22 PM mma 5 2,075 (E, B, V) a vector bundle.EndE is the set of endomorphisms of E, then if g belongs EndE therefore g is a linear V-> V... Oct12-10 06:21 AM quasar987 1 753 Well really.... how do you figure it out? Thanks for your help. Apr24-05 03:28 PM dextercioby 1 1,546 Since there are some equations in my question. I write my question in the following attachment. It is about the... Jan24-05 04:09 PM dextercioby 4 4,530 I'm looking for help understanding the coordinate ring. The definition I have roughly says There is a surjection ... Apr7-10 12:30 PM andlook 0 1,420 Hi, I'm trying to understand the fiber bundle formulation of gauge theory at the moment, and I'm stuck on the... Nov29-12 09:07 PM ...? 2 1,039 This may seem like a foolish question, but I can't seem to find the answer anywhere. Also, please forgive the question... Nov10-10 11:56 AM Kreizhn 4 1,130 Unless I'm mistaken about something, the Bing metrization theorem is more or less only a corrolary of the... Dec31-10 10:50 AM radou 2 1,570 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 4 993 In considering the shortest paths between two points on a sphere I came across the following interesting problem: ... Sep9-14 04:15 AM nixed 14 476 Hi I do 3D modeling and lately i have been trying to make some more theoretic diagrams about the whole thing.... May10-11 01:29 AM Unrest 3 1,340 Hi! I'm perusing fractals out of personal interest. Although I come from physics, I have a background in math-major... May20-09 05:29 PM squidsoft 1 2,054 Hi. I was wondering if you guys can refer me to the best possible text that teaches the computations in tensor... Jan5-07 02:02 PM chroot 31 13,131 Hello All, I'm programming an applet and run over a problem I can't solve (hope this is the right place to post... Apr19-12 04:47 AM bitttttor 10 1,971 Howdy all! I've been wracking (or wrecking) my brain trying to figure out how one might stack tesseracts. If I... Oct12-08 10:33 AM snathi 0 1,546 Hi forum, I was having some difficulty in understanding how time as a fourth dimension allows a cube of three spatial... Jun25-10 03:10 PM SonyAD 13 3,624 somebody know some link or ebook about tensor with examples solved and execises Nov16-07 06:12 PM robphy 1 1,684 Hello, can anyone explain simply what is a tensor, using the language of Geometric Algebra? Thanks! Jun10-09 06:03 AM SW VandeCarr 7 2,499 Can anyone recommend good introductory texts for self-study? I want to teach myself about tensors and about topology.... Nov12-05 06:07 PM robphy 2 1,549 Greetings Gurus, I'm sure this has been asked before, so feel free to redirect me. What is the connection... Jan8-06 10:56 AM mathwonk 7 4,276 Do any of you have the book Tensors & Manifolds, by Robert H. Wasserman? I was looking for another good book on... Jun20-07 10:57 PM pmb_phy 0 1,897 I've heard alot about "lie groups" on this section of the forum, and was wondering what they are and if someone could... Feb6-05 12:54 AM mathwonk 9 2,983 I'm currently researching a 3d tensor, where certain combinations of terms can cause the principal values... Dec7-06 05:29 AM desA 2 1,813 I am having trouble understanding how to tell if a matrix is a tensor, a pseudo tensor or neither or the above. Given... Feb21-11 03:26 PM Marthius 2 1,940 Definitions like this one are common in books: For all ##k,l\in\mathbb N##, a multilinear map... Jun13-13 08:13 PM Fredrik 11 2,598 Hello, I would very much like someone to please clarify the following points concerning tensor summation to me.... Jul15-13 09:31 AM HallsofIvy 11 2,563 I have been trying to learn and visualize a bit of tensor algebra recently, and have been confused by the... Jan9-11 11:19 PM MadRocketSci2 0 1,755 1. When can I contract a tensor? Is that an option to contract for example a (1, 1) tensor to a real number or has... Jan24-06 12:14 PM mathwonk 16 3,598 I've been wracking my brains trying to answer this but it's just really hard. If some one could help me out I would... Nov27-08 02:10 PM shoehorn 1 1,462 Hi all, What is a good introductory book on tensor products and tensor algebras? For motivation, I have found Tom... Mar20-07 07:06 AM George Jones 1 12,397 I've searched everywhere about tensor products but I just can't understand them. Can anyone please explain this... Apr24-11 01:23 AM dimension10 10 2,428 Hello, I have an exercise where we have to pullback a metric g^{ij} \, \mathrm dx_i \, \mathrm dx_j under a... Feb25-08 02:53 PM Fredrik 3 3,060 It's possible to do the tensor product of two contravariant vectors? It's possible to do the tensor product of two... Aug10-04 01:43 PM mathwonk 5 3,137 Could someone tell me what the tensor product is and give an example? Feb18-07 08:28 PM pmb_phy 1 2,203 what is the tensor product's physical significance? I know what it does mathematically, but what does it mean. I have... Dec4-07 07:03 AM mathwonk 17 5,832 Hi, I have a quick question about a derivation that has annoyed me all day. I am trying to prove, from the definition... Dec11-07 09:48 AM cathalcummins 3 1,784 Excercise Exercise 1.6 of Roger Blandford and Kip Thorne's online textbook Applications of Classical Physics: "In... Nov7-09 12:18 AM Rasalhague 2 1,065 Hello everyone! I finished school 2 months ago and at the moment I'm looking forward to my study in physics :) ... Jul26-08 03:48 PM ForMyThunder 3 9,952