Difference between revisions of "Affine torsion"
From Encyclopedia of Mathematics
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One of the differential invariants of a curve in equi-affine space: | One of the differential invariants of a curve in equi-affine space: | ||
| − | + | $$ | |
| + | \tau = - ( \mathbf r ^ {\prime\prime} , \mathbf r ^ {\prime\prime\prime} ,\ | ||
| + | \mathbf r ^ {\prime\prime\prime\prime} ) , | ||
| + | $$ | ||
where the primes denote differentiation with respect to the affine parameter of the position vector of the curve. Similar concepts are introduced for curves in spaces with other fundamental groups such as centro-affine. | where the primes denote differentiation with respect to the affine parameter of the position vector of the curve. Similar concepts are introduced for curves in spaces with other fundamental groups such as centro-affine. | ||
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====Comments==== | ====Comments==== | ||
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====References==== | ====References==== | ||
<table><TR><TD valign="top">[1]</TD> <TD valign="top"> S. Buchin, "Affine differential geometry" , Sci. Press and Gordon & Breach (1983)</TD></TR></table> | <table><TR><TD valign="top">[1]</TD> <TD valign="top"> S. Buchin, "Affine differential geometry" , Sci. Press and Gordon & Breach (1983)</TD></TR></table> | ||
Revision as of 16:09, 1 April 2020
One of the differential invariants of a curve in equi-affine space:
$$ \tau = - ( \mathbf r ^ {\prime\prime} , \mathbf r ^ {\prime\prime\prime} ,\ \mathbf r ^ {\prime\prime\prime\prime} ) , $$
where the primes denote differentiation with respect to the affine parameter of the position vector of the curve. Similar concepts are introduced for curves in spaces with other fundamental groups such as centro-affine.
Comments
References
| [1] | S. Buchin, "Affine differential geometry" , Sci. Press and Gordon & Breach (1983) |
How to Cite This Entry:
Affine torsion. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Affine_torsion&oldid=45050
Affine torsion. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Affine_torsion&oldid=45050
This article was adapted from an original article by A.P. Shirokov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article