Home > Metrics and forms
Tensors and Relativity: Chapter 3

Metrics and forms

next up previous index
Next: One- forms Up: Title page Previous: Title page

Recall that the scalar product of two four- vectors is tex2html_wrap_inline1690 :

equation1154

so

equation1160

where

eqnarray1166

are the components of the metric tensor .

We can think of the metric tensor as a map  which takes two four- vectors tex2html_wrap_inline1692 and tex2html_wrap_inline1694 into the reals: tex2html_wrap_inline1696 .

The map is linear in the arguments, in the sense that

equation1180

We can generalize this by defining a tensor of type 0/N as a map which takes N four- vectors into the reals which is linear in all its arguments, for example the metric tensor  is a type 0/2 tensor.


TOP