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Line Element

Also known as the first Fundamental Form

\begin{displaymath}
ds^2=g_{ab}\,dx^a\,dx^b.
\end{displaymath}

In the principal axis frame for 3-D,

\begin{displaymath}
ds^2=g_{aa}(dx^a)^2+g_{bb}(dx^b)^2+g_{cc}(dx^c)^2.
\end{displaymath}

At Ordinary Points on a surface, the line element is positive definite.

See also Area Element, Fundamental Forms, Volume Element




© 1996-9 Eric W. Weisstein
1999-05-25