One Forms

  • Thread starter Jomapil
  • Start date
  • #1
14
0
Hello, everyone

I began do learn Relativity Theory. I don't understand the term " One Forms " that appear in some books. Can anyone tell me what did it mean? The translation to Portuguese doesn't any sense and the explanation of the books is not very explicative for me.

Thank you very much.
 

Answers and Replies

  • #2
136
0
''One forms'' are a mathematical lingo for a linear function that takes a vector and returns a scalar; it's therefore a type of tensor.
 
  • #3
dx
Homework Helper
Gold Member
2,011
18
1-forms are the geometric objects corresponding to the local linear behavior of functions on a manifold.

If a patch of a manifold M is described by the coordinate functions xi : M → R, then for any function f on that patch, its local linear behavior can be given a coordinate representation in terms of the coordinate 1-forms dxi thus: df = ∑(∂f/∂xi)dxi, where the numnbers ∂f/∂xi are called the components of df.

For more details I recommend these books: "Applied Differential Geometry" and "Spacetime, Geometry and Cosmology" by William Burke.
 
  • #4
haushofer
Science Advisor
Insights Author
2,472
860
A one-form is exactly the same as what other people call "a covariant vector". :) But to understand this you need some basis in tensor analysis.
 
  • #5
14
0
Good evening.

haushofer - I studied tensor calculus 35 years ago and I'm reading and exercising at the same time I'm learning Relativity Theory, so I understand your explanation - EVERY covariant tensor is an One-Form.

ManyNames - I think I understood your explanation - for example the operator divergence [ div(vctor) --> escalar] is an One-Forms.

dx - I'm going soon to read about manifolds - anyway I also understood your help.

Thank you everyone and a good new week.
 

Related Threads on One Forms

  • Last Post
Replies
1
Views
2K
  • Last Post
2
Replies
26
Views
12K
  • Last Post
2
Replies
27
Views
5K
  • Last Post
Replies
9
Views
850
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
17
Views
2K
  • Last Post
Replies
5
Views
4K
Replies
2
Views
860
Replies
8
Views
1K
  • Last Post
Replies
5
Views
2K
Top