Two-point tensor
From Encyclopedia of Mathematics
A tensor 
which depends on a pair of points 
in a manifold 
, i.e. a tensor field 
defined on the product 
. As an example, covariant derivatives of the world function 
and, in general, of an arbitrary invariant depending on two points are two-point tensors. The properties of such a tensor, in particular the limits of 
and its derivatives as 
, such as
 |
are employed in the calculus of variations and in the theory of relativity.
References
| [1] | J.L. Synge, "Relativity: the general theory" , North-Holland & Interscience (1960) |
How to Cite This Entry:
Two-point tensor. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Two-point_tensor&oldid=13796
Two-point tensor. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Two-point_tensor&oldid=13796
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article