Bifurcations of affine invariants for one-parameter family of generic convex plane curves

Takashi Sano

Banach Center Publications (1999)

  • Volume: 50, Issue: 1, page 227-236
  • ISSN: 0137-6934

Abstract

top
We study affine invariants of plane curves from the view point of the singularity theory of smooth functions. We describe how affine vertices and affine inflexions are created and destroyed.

How to cite

top

Sano, Takashi. "Bifurcations of affine invariants for one-parameter family of generic convex plane curves." Banach Center Publications 50.1 (1999): 227-236. <http://eudml.org/doc/209011>.

@article{Sano1999,
abstract = {We study affine invariants of plane curves from the view point of the singularity theory of smooth functions. We describe how affine vertices and affine inflexions are created and destroyed.},
author = {Sano, Takashi},
journal = {Banach Center Publications},
keywords = {plane curves; affine distance function; affine height function; bifurcation},
language = {eng},
number = {1},
pages = {227-236},
title = {Bifurcations of affine invariants for one-parameter family of generic convex plane curves},
url = {http://eudml.org/doc/209011},
volume = {50},
year = {1999},
}

TY - JOUR
AU - Sano, Takashi
TI - Bifurcations of affine invariants for one-parameter family of generic convex plane curves
JO - Banach Center Publications
PY - 1999
VL - 50
IS - 1
SP - 227
EP - 236
AB - We study affine invariants of plane curves from the view point of the singularity theory of smooth functions. We describe how affine vertices and affine inflexions are created and destroyed.
LA - eng
KW - plane curves; affine distance function; affine height function; bifurcation
UR - http://eudml.org/doc/209011
ER -

References

top
  1. [1] V. I. Arnol'd, Wave front evolution and equivariant Morse lemma, Comm. Pure Appl. Math. 29 (1976), 557-582. Zbl0343.58003
  2. [2] W. Blaschke, Vorlesungen über Differentialgeometrie II, Springer, Berlin, 1923. Zbl49.0499.01
  3. [4] J. W. Bruce, Isotopies of generic plane curves, Glasgow Math. J. 24 (1983), 195-206. Zbl0513.58007
  4. [3] J. W. Bruce and P. J. Giblin, Curves and Singularities. A Geometrical Introduction to Singularity Theory, Cambridge Univ. Press, Cambridge, 1984. Zbl0534.58008
  5. [6] D. L. Fidal, The existence of sextactic points, Math. Proc. Cambridge Philos. Soc. 96 (1984), 433-436. Zbl0568.58007
  6. [5] D. L. Fidal and P. J. Giblin, Generic 1-parameter families of caustics by reflexion in the plane, Math. Proc. Cambridge Philos. Soc. 96 (1984), 425-432. Zbl0561.58004
  7. [7] C. G. Gibson, Singular Points of Smooth Mappings, Pitman Research Notes in Mathematics 25, Pitman Publ., London, 1979. Zbl0426.58001
  8. [8] S. Izumiya and T. Sano, Generic affine differential geometry of plane curves, Proc. Edinburgh Math. Soc. (2) 41 (1998), 315-324. Zbl0965.53013
  9. [9] K. Nomizu and T. Sasaki, Affine Differential Geometry. Geometry of Affine Immersions, Cambridge Tracts in Math. 111, Cambridge Univ. Press, Cambridge, 1994. Zbl0834.53002

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.