A BASIS OF THE SPACE OF MEROMORPHIC QUADRATIC DIFFERENTIALS ON RIEMANN SURFACES

  • Keum, J.H. (Department of Mathematics Konkuk University ) ;
  • Lee, M.K. (Department of Mathematics Kongyang University)
  • 발행 : 1998.02.01

초록

It is proved [6] that there exists a basis of $L^\Gamma$ (the space of meromorphic vector fields on a Riemann surface, holomorphic away from two fixed points) represented by the vector fields which have the expected zero or pole order at the two points. In this paper, we carry out the same task for the quadratic differentials. More precisely, we compute a basis of $Q^\Gamma$ (the sapce of meromorphic quadratic differentials on a Riemann surface, holomorphic away from two fixed points). This basis consists of the quadratic differentials which have the expected zero or pole order at the two points. Furthermore, we show that $Q^\Gamma$ has a Lie algebra structure which is induced from the Krichever-Novikov algebra $L^\Gamma$.

키워드

참고문헌

  1. Riemann surfaces H.M. Farkas;I. Kra
  2. Lectures on Riemann Surfaces O. Frester
  3. Funk. Anal. i. Pril. v.21 Algebras of Virasoro Type, Riemann Surfaces and Structures of the Theory of Solitons I.M. Krichever;S.P. Novikov
  4. Funk Anal. i. Pril. v.21 Virasora Type Algebras, Riemann Surfaces and Strings in Minkowski Space I.M. Krichever;S.P. Novikov
  5. Compact Riemann Surfaces R. Narasimhan
  6. Lecture Notes in Physics An Introduction to Riemann Surfaces, Algebraic Curves and Moduli Spaces M. Schlichenmaier