Open AccessGeodesic scattering on hyperboloids and Knörrer’s map
Author(s) -
А. П. Веселов,
Lihua Wu
Publication year - 2021
Publication title -
nonlinearity
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.571
H-Index - 90
eISSN - 1361-6544
pISSN - 0951-7715
DOI - 10.1088/1361-6544/ac0f4e
Subject(s) - geodesic , mathematics , metric (unit) , closure (psychology) , pure mathematics , relation (database) , mathematical analysis , geometry , algebra over a field , computer science , market economy , operations management , database , economics
We use the results of Moser and Knörrer on relations between geodesics on quadrics and solutions of the classical Neumann system to describe explicitly the geodesic scattering on hyperboloids. We explain the relation of Knörrer’s reparametrisation with projectively equivalent metrics on quadrics introduced by Tabachnikov and independently by Matveev and Topalov, giving a new proof of their result. We show that the projectively equivalent metric is regular on the projective closure of hyperboloids and extend Knörrer’s map to this closure.