Bifurcation sets of families of reflections on surfaces in R<SUP>3</SUP>

Giblin, PJ and Janeczko, S (2017) Bifurcation sets of families of reflections on surfaces in R<SUP>3</SUP>. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 147 (2). pp. 337-352.

Text M:\Warsaw\research\2014 paper\giblin-janeczko-draft8.pdf - Author Accepted Manuscript Download (214kB)

Abstract

<jats:p>We introduce a new affinely invariant structure on smooth surfaces in ℝ<jats:sup>3</jats:sup> by defining a family of reflections in all points of the surface. We show that the bifurcation set of this family has a special structure at ‘<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0308210516000184_inline01" /> points’, which are not detected by the flat geometry of the surface. These <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0308210516000184_inline01" /> points (without an associated structure on the surface) have also arisen in the study of the centre symmetry set; using our technique we are able to explain how the points are created and annihilated in a generic family of surfaces. We also present the bifurcation set in a global setting.</jats:p>

Item Type:	Article
Uncontrolled Keywords:	affine invariants, surfaces, parabolic sets, bifurcation sets
Depositing User:	Symplectic Admin
Date Deposited:	23 Aug 2017 10:09
Last Modified:	10 Oct 2023 22:23
DOI:	10.1017/S0308210516000184
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3009100