# Affine surfaces with parallel shape operators

Annales Polonici Mathematici (1992)

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

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topWłodzimierz 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] F. Dillen, Locally symmetric complex affine hypersurfaces, J. Geom. 33 (1988), 27-38. Zbl0656.53012
- [2] F. Dillen, Equivalence theorems in affine differential geometry, Geom. Dedicata 32 (1989), 81-92. Zbl0684.53012
- [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] K. Nomizu, On completeness in affine differential geometry, Geom. Dedicata 20 (1986), 43-49. Zbl0587.53010
- [5] K. Nomizu and U. Pinkall, On the geometry of affine immersions, Math. Z. 195 (1987), 165-178. Zbl0629.53012
- [6] K. Nomizu and U. Pinkall, Cayley surfaces in affine differential geometry, Tôhoku Math. J. 41 (1989), 589-596.

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