Geodesic
Geometry of a Doubly Canal Hypersurface in the Euclidean Space $\mathbb E^n$
Matematičeskie trudy, Tome 6 (2003) no. 1, pp. 169-181 
M. A. Cheshkova. Geometry of a Doubly Canal Hypersurface in the Euclidean Space $\mathbb E^n$. Matematičeskie trudy, Tome 6 (2003) no. 1, pp. 169-181. http://geodesic.mathdoc.fr/item/MT_2003_6_1_a6/
@article{MT_2003_6_1_a6,
     author = {M. A. Cheshkova},
     title = {Geometry of {a~Doubly} {Canal} {Hypersurface} in {the~Euclidean} {Space~}$\mathbb E^n$},
     journal = {Matemati\v{c}eskie trudy},
     pages = {169--181},
     year = {2003},
     volume = {6},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MT_2003_6_1_a6/}
}
TY  - JOUR
AU  - M. A. Cheshkova
TI  - Geometry of a Doubly Canal Hypersurface in the Euclidean Space $\mathbb E^n$
JO  - Matematičeskie trudy
PY  - 2003
SP  - 169
EP  - 181
VL  - 6
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/MT_2003_6_1_a6/
LA  - ru
ID  - MT_2003_6_1_a6
ER  - 
%0 Journal Article
%A M. A. Cheshkova
%T Geometry of a Doubly Canal Hypersurface in the Euclidean Space $\mathbb E^n$
%J Matematičeskie trudy
%D 2003
%P 169-181
%V 6
%N 1
%U http://geodesic.mathdoc.fr/item/MT_2003_6_1_a6/
%G ru
%F MT_2003_6_1_a6

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider a multidimensional analog in $\mathbb E^n$ to Dupin cyclides, that is, surfaces whose principal curvatures are constant along the corresponding principal directions. We study doubly canal hypersurfaces, i. e., hypersurfaces having two principal curvatures of multiplicities $p$ and $q$ with $p+q=n-1$.

[1] Atanasyan L. S., Bazylev V. T., Geometriya, t. 2, Prosveschenie, M., 1986

[2] Vyalyas M. E., Lumiste Yu. G., “Izotermicheskie giperpoverkhnosti i trekhmernye gipertsiklidy Dyupena — Manngeima”, Mat. zametki, 41:5 (1987), 731–740 | MR | Zbl

[3] Kobayasi Sh., Nomidzu K., Osnovy differentsialnoi geometrii, t. 2, Nauka, M., 1981 | MR

[4] Lumiste Yu. G., “Konstruktsiya Keli — Katalana dlya nekotorykh giperpoverkhnostei Dyupena”, Uch. zap. Tartussk. un-ta, 734, 1986, 36–49 | Zbl

[5] Cheshkova M. A., “Dvazhdy kanalovye giperpoverkhnosti v evklidovom prostranstve”, Mat. sb., 191:6 (2000), 155–160 | MR | Zbl

[6] Shulikovskii V. I., Klassicheskaya differentsialnaya geometriya, GIFML, M., 1963

[7] Cecil T. E., Ryan P. J., “Conformal geometry and cyclides of Dupin”, Canad. J. Math., 32:4 (1980), 767–782 | MR | Zbl

[8] Pinkall U., “Dupin'sche Hyperflachen in $\mathbb E^4$”, Manuscripta Math., 51 (1985), 89–119 | DOI | MR | Zbl