Abstract
We use the concept of measure of symmetry for ovals to generalize the notion of center of symmetry. We show that for generic plane convex curves the center symmetry set has only fold and cusp singularities.
Similar content being viewed by others
References
Bruce, J. W. and Giblin, P. J.: Curves and Singularities (2nd edn), Cambridge University Press, 1992.
Bruce, J. W., Giblin, P. J. and Gibson, C. G., Genericity of caustics by reflection, AMS Proc. Symp. Pure Math 40, Part I (1983), 179–193.
Grünbaum, B.: Measures of symmetry for convex sets, AMS Proc. Symp. Pure Math. 7 (Convexity), Providence, 1963, pp. 233–270.
Stewart, B. M.: Asymmetry of a plane convex set with respect to its centroid, Pacific J. Math. 8 (1958), 335–337.
de Valcourt, B. A.: Measures of axial symmetry for ovals, Israel J. Math. 4 (1966), 65–82.
Wall, C. T. C.: Geometric properties of generic differentiable manifolds, in Geometry and Topology III, Springer Lecture Notes in Maths 597 (1976), 707–774.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Janeczko, S. Bifurcations of the center of symmetry. Geom Dedicata 60, 9–16 (1996). https://doi.org/10.1007/BF00150864
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00150864