GEOMETRIC INVARIANTS ASSOCIATED WITH PROJECTIVE STRUCTURES AND UNIVALENCE CRITERIA

• KIM SEONG-A

  Department of Mathematics Education, Dongguk University

• SUGAWA TOSHIYUKI

  Graduate School of Information Sciences, Tohoku University

Abstract

For a nonconstant holomorphic map between projective Riemann surfaces with conformal metrics, we consider invariant Schwarzian derivatives and projective Schwarzian derivatives of general virtual order. We show that these two quantities are related by the “Schwarzian derivative” of the metrics of the surfaces (at least for the case of virtual orders 2 and 3). As an application, we give univalence criteria for a meromorphic function on the unit disk in terms of the projective Schwarzian derivative of virtual order 3.

Journal

• Tohoku Mathematical Journal, Second Series

  Tohoku Mathematical Journal, Second Series 63 (1), 41-57, 2011

  Mathematical Institute, Tohoku University

Keywords

• Schwarzian derivative
• conformal metric
• univalence criterion

Details

• CRID: 1390001205117771008
• NII Article ID: 110008425968
• NII Book ID: AA00863953
• DOI: 10.2748/tmj/1303219935
• ISSN: 2186585X
• ISSN: 00408735
• Text Lang: en
• Data Source:
  • JaLC
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed