Morse index of a cyclic polygon

• Autorzy: Gaiane Panina , Alena Zhukova
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Morse index; Linkage; Moduli space; Cyclic polygon

Kategorie tematyczne

• 52B99: None of the above, but in this section
• 57R70: Critical points and critical submanifolds

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2011
• Tom: 9
• Numer: 2
• Strony: 364-377

Daty

wydano

2011-04-01

online

2011-02-18

Twórcy

autor

Gaiane Panina

• St. Petersburg Institute for Informatics and Automation of RAS

autor

Alena Zhukova

• St. Petersburg State University

Bibliografia

• [1] Cerf J., La stratification naturelle des espaces de fonctions différentiables réelles et le théorème de la pseudo-isotopie, Publ. Math. Inst. Hautes Études Sci., 1970, 39, 5–173 http://dx.doi.org/10.1007/BF02684687
• [2] Elerdashvili E., Jibladze M., Khimshiashvili G., Cyclic configurations of pentagon linkages, Bull. Georgian Acad. Sci., 2008, 2(4), 29–32
• [3] Farber M., Schütz, D., Homology of planar polygon spaces, Geom. Dedicata, 2007, 125(1), 75–92. http://dx.doi.org/10.1007/s10711-007-9139-7
• [4] Khimshiashvili G., Configuration spaces and signature formulas, J. Math. Sci. (N. Y.), 2009, 160(6), 727–736 http://dx.doi.org/10.1007/s10958-009-9524-x
• [5] Panina G., Khimshiashvili G., Cyclic polygons are critical points of area, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI), 2008, 360, 238–245
• [6] Pólya G., Mathematics and Plausible Reasoning. Vol. 1: Induction and Analogy in Mathematics, Princeton University Press, Princeton, 1954
• [7] Zvonkine D., Configuration spaces of hinge constructions. Russ. J. Math. Phys., 1997, 5(2), 247–266

Identyfikatory

DOI

10.2478/s11533-011-0011-5