Affine surfaces with parallel shape operators

Włodzimierz Jelonek

Annales Polonici Mathematici (1992)

  • Volume: 56, Issue: 2, page 179-186
  • ISSN: 0066-2216

Abstract

top
We study affine nondegenerate Blaschke hypersurfaces whose shape operators are parallel with respect to the induced Blaschke connections. We classify such surfaces and thus give an exact classification of extremal locally symmetric surfaces, first described by F. Dillen.

How to cite

top

Włodzimierz Jelonek. "Affine surfaces with parallel shape operators." Annales Polonici Mathematici 56.2 (1992): 179-186. <http://eudml.org/doc/262305>.

@article{WłodzimierzJelonek1992,
abstract = {We study affine nondegenerate Blaschke hypersurfaces whose shape operators are parallel with respect to the induced Blaschke connections. We classify such surfaces and thus give an exact classification of extremal locally symmetric surfaces, first described by F. Dillen.},
author = {Włodzimierz Jelonek},
journal = {Annales Polonici Mathematici},
keywords = {Blaschke structure; affine locally symmetric surface; affine shape operator; equiaffine structure; affine normal field; extremal locally symmetric surfaces; affine Blaschke surfaces; shape operator},
language = {eng},
number = {2},
pages = {179-186},
title = {Affine surfaces with parallel shape operators},
url = {http://eudml.org/doc/262305},
volume = {56},
year = {1992},
}

TY - JOUR
AU - Włodzimierz Jelonek
TI - Affine surfaces with parallel shape operators
JO - Annales Polonici Mathematici
PY - 1992
VL - 56
IS - 2
SP - 179
EP - 186
AB - We study affine nondegenerate Blaschke hypersurfaces whose shape operators are parallel with respect to the induced Blaschke connections. We classify such surfaces and thus give an exact classification of extremal locally symmetric surfaces, first described by F. Dillen.
LA - eng
KW - Blaschke structure; affine locally symmetric surface; affine shape operator; equiaffine structure; affine normal field; extremal locally symmetric surfaces; affine Blaschke surfaces; shape operator
UR - http://eudml.org/doc/262305
ER -

References

top
  1. [1] F. Dillen, Locally symmetric complex affine hypersurfaces, J. Geom. 33 (1988), 27-38. Zbl0656.53012
  2. [2] F. Dillen, Equivalence theorems in affine differential geometry, Geom. Dedicata 32 (1989), 81-92. Zbl0684.53012
  3. [3] M. Magid and K. Nomizu, On affine surfaces whose cubic forms are parallel relative to the affine metric, Proc. Nat. Acad. Sci. U.S.A. 65 (1989), 215-218. Zbl0705.53010
  4. [4] K. Nomizu, On completeness in affine differential geometry, Geom. Dedicata 20 (1986), 43-49. Zbl0587.53010
  5. [5] K. Nomizu and U. Pinkall, On the geometry of affine immersions, Math. Z. 195 (1987), 165-178. Zbl0629.53012
  6. [6] K. Nomizu and U. Pinkall, Cayley surfaces in affine differential geometry, Tôhoku Math. J. 41 (1989), 589-596. 

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.