Research Article

Central European Journal of Mathematics

, Volume 9, Issue 2, pp 364-377

Morse index of a cyclic polygon

  • Gaiane PaninaAffiliated withSt. Petersburg Institute for Informatics and Automation of RAS Email author 
  • , Alena ZhukovaAffiliated withSt. Petersburg State University

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Abstract

It is known that cyclic configurations of a planar polygonal linkage are critical points of the signed area function. In the paper we give an explicit formula of the Morse index for the signed area of a cyclic configuration. We show that it depends not only on the combinatorics of a cyclic configuration, but also on its metric properties.

Keywords

Morse index Linkage Moduli space Cyclic polygon

MSC

52B99 57R70