Difference between revisions of "Bilinear differential"
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| − | where | + | An analytic [[Differential on a Riemann surface|differential on a Riemann surface]], depending on two points $ P $ |
| + | and $ Q $, | ||
| + | and having the form | ||
| + | |||
| + | $$ | ||
| + | f (z, \zeta ) dz d \zeta , | ||
| + | $$ | ||
| + | |||
| + | where $ z $ | ||
| + | and $ \zeta $ | ||
| + | are local uniformizing parameters in a neighbourhood of $ P $ | ||
| + | and $ Q $ | ||
| + | respectively, and $ f(z, \zeta ) $ | ||
| + | is an analytic function of $ z $ | ||
| + | and $ \zeta $. | ||
| + | Bilinear differentials are used to express many functionals on a [[Finite Riemann surface|finite Riemann surface]]. | ||
====References==== | ====References==== | ||
<table><TR><TD valign="top">[1]</TD> <TD valign="top"> M. Schiffer, D.C. Spencer, "Functionals of finite Riemann surfaces" , Princeton Univ. Press (1954)</TD></TR></table> | <table><TR><TD valign="top">[1]</TD> <TD valign="top"> M. Schiffer, D.C. Spencer, "Functionals of finite Riemann surfaces" , Princeton Univ. Press (1954)</TD></TR></table> | ||
Latest revision as of 10:59, 29 May 2020
An analytic differential on a Riemann surface, depending on two points $ P $
and $ Q $,
and having the form
$$ f (z, \zeta ) dz d \zeta , $$
where $ z $ and $ \zeta $ are local uniformizing parameters in a neighbourhood of $ P $ and $ Q $ respectively, and $ f(z, \zeta ) $ is an analytic function of $ z $ and $ \zeta $. Bilinear differentials are used to express many functionals on a finite Riemann surface.
References
| [1] | M. Schiffer, D.C. Spencer, "Functionals of finite Riemann surfaces" , Princeton Univ. Press (1954) |
How to Cite This Entry:
Bilinear differential. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Bilinear_differential&oldid=19114
Bilinear differential. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Bilinear_differential&oldid=19114
This article was adapted from an original article by E.D. Solomentsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article