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
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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=30204
Two-point tensor. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Two-point_tensor&oldid=30204
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article