46 research outputs found
The Weierstrass-Enneper Representation using hodographic coordinates on a minimal surface
In this paper we obtain the general solution to the minimal surface equation,
namely its local Weierstrass-Enneper representation, by using a system of
hodographic coordinates. This is done by using the method of solving the
Born-Infeld equations by Whitham. We directly compute conformal coordinates on
the minimal surface which give the Weierstrass-Enneper representation. From
this we derive the hodographic coordinate \rho \in D \subset {\CC} and
its complex conjugate which enables us to write the
Weierstrass-Enneper representation in a new way.Comment: 5-pages, semi-expository article, published in Proceedings of the
Indian Academy of Sciences, 2003 (an electronic journal
Holomorphic Quillen determinant line bundles on integral compact Kahler manifolds
We show that any compact Kahler manifold with integral Kahler form,
parametrizes a natural holomorphic family of Cauchy-Riemann operators on the
Riemann sphere such that the Quillen determinant line bundle of this family is
isomorphic to a sufficiently high tensor power of the holomorphic line bundle
determined by the integral Kahler form. We also establish a symplectic version
of the result. We conjecture that an equivariant version of our result is true.Comment: Latex2e, 10 pages, To appear in, Quillen memorial issue, Quarterly J.
Mat