My Math Forum  

Go Back   My Math Forum > College Math Forum > Real Analysis

Real Analysis Real Analysis Math Forum


Reply
 
LinkBack Thread Tools Display Modes
May 1st, 2009, 07:23 PM   #1
Newbie
 
Joined: May 2009

Posts: 1
Thanks: 0

vector field

A vector field in the usual torus T is obtained by parametrizing the meridians of T by arc length and defining w(p) as the velocity vector of the meridian through p. Prove that the vector field is differentiable.
vv19882000 is offline  
 
July 2nd, 2009, 03:44 PM   #2
Member
 
Rebesques's Avatar
 
Joined: Aug 2007

Posts: 42
Thanks: 4

Re: vector field

Consider a point on , a coordinate neighbourhood of and (a section of a) meridian contained in .If is the tangent vector at , then . Along , there is an obvious choice of orthonormal bases for the tangent spaces .

Consider now a differentiable function . If is differentiable at for all such , then is differentiable. To this end, express . Since is differentiable, we have for some differentiable at functions . Therefore ,
which proves that is differentiable at .
Rebesques is offline  
Reply

  My Math Forum > College Math Forum > Real Analysis

Tags
field, vector



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Vector field Uniman Linear Algebra 2 October 19th, 2012 08:32 AM
Vector Calculus Divergence of a Vector Field MasterOfDisaster Calculus 2 September 26th, 2011 09:17 AM
Vector Field 3 OSearcy4 Calculus 9 October 29th, 2009 06:09 AM
Vector Field 2 OSearcy4 Calculus 2 October 27th, 2009 06:39 PM
Vector Field OSearcy4 Calculus 0 October 27th, 2009 12:05 PM





Copyright © 2019 My Math Forum. All rights reserved.