Zobrazeno 1 - 10
of 96
pro vyhledávání: '"Thomas E. Cecil"'
Autor:
Thomas E. Cecil
Publikováno v:
Axioms, Vol 13, Iss 6, p 399 (2024)
A hypersurface M in Rn or Sn is said to be Dupin if along each curvature surface, the corresponding principal curvature is constant. A Dupin hypersurface is said to be proper Dupin if each principal curvature has constant multiplicity on M, i.e., the
Externí odkaz:
https://doaj.org/article/af5acb4afc7a4108893455b5f522b341
Autor:
Thomas E. Cecil
A hypersurface $M$ in ${\bf R}^n$ is said to be Dupin if along each curvature surface, the corresponding principal curvature is constant. A Dupin hypersurface is said to be proper Dupin if the number of distinct principal curvatures is constant on $M
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7ecfa817b40e9d6321914c1ec8752ed7
Autor:
Thomas E. Cecil
Publikováno v:
Symmetry, Integrability and Geometry: Methods and Applications, Vol 4, p 062 (2008)
A hypersurface $M^{n−1}$ in a real space-form $R^n$, $S^n$ or $H^n$ is isoparametric if it has constant principal curvatures. For $R^n$ and $H^n$, the classification of isoparametric hypersurfaces is complete and relatively simple, but as Élie Car
Externí odkaz:
https://doaj.org/article/f5b15645040f422f8a2915dd78397f33
Autor:
Thomas E. Cecil, Patrick J. Ryan
This exposition provides the state-of-the art on the differential geometry of hypersurfaces in real, complex, and quaternionic space forms. Special emphasis is placed on isoparametric and Dupin hypersurfaces in real space forms as well as Hopf hypers
Publikováno v:
Pacific Journal of Mathematics. 234:229-247
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::c3d8270f20460e5f5e5bf662b72945eb
https://doi.org/10.2140/pjm.2008.234.229
https://doi.org/10.2140/pjm.2008.234.229
Publikováno v:
Geometriae Dedicata. 128:55-95
If M is an isoparametric hypersurface in a sphere S n with four distinct principal curvatures, then the principal curvatures κ1, . . . , κ4 can be ordered so that their multiplicities satisfy m 1 = m 2 and m 3 = m 4, and the cross-ratio r of the pr
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::afdcd752eab0f993238536fd92cb4f3e
https://doi.org/10.1007/s10711-007-9183-3
https://doi.org/10.1007/s10711-007-9183-3
Publikováno v:
Annals of Mathematics. 166:1-76
Let M be an isoparametric hypersurface in the sphere S n with four distinct principal curvatures. Munzner showed that the four principal curvatures can have at most two distinct multiplicities m1 ,m 2, and Stolz showed that the pair (m1 ,m 2) must ei
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::dc6b8b694e417da1d8b02216f608df2b
https://doi.org/10.4007/annals.2007.166.1
https://doi.org/10.4007/annals.2007.166.1
Autor:
Thomas E. Cecil, Patrick J. Ryan
Publikováno v:
Springer Monographs in Mathematics ISBN: 9781493932450
This chapter is an outline of the method for studying submanifolds of Euclidean space R n or the sphere S n in the context of Lie sphere geometry. For Dupin hypersurfaces this has proven to be a valuable approach, since Dupin hypersurfaces occur natu
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::b77874087f30bedd1bcee7c1ce9088da
https://doi.org/10.1007/978-1-4939-3246-7_4
https://doi.org/10.1007/978-1-4939-3246-7_4
Autor:
Thomas E. Cecil, Patrick J. Ryan
Publikováno v:
Springer Monographs in Mathematics ISBN: 9781493932450
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::16677ac23bce97705b35a10c67ded84d
https://doi.org/10.1007/978-1-4939-3246-7
https://doi.org/10.1007/978-1-4939-3246-7
Autor:
Patrick J. Ryan, Thomas E. Cecil
Publikováno v:
Springer Monographs in Mathematics ISBN: 9781493932450
In 1986, Martinez and Perez [470] began the study of real hypersurfaces in quaternionic space forms, and in 1991, Berndt [31] found a list of standard examples of real hypersurfaces in quaternionic space forms with constant principal curvatures, lead
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::63d5d32084fcf9d2322188546a44f0bf
https://doi.org/10.1007/978-1-4939-3246-7_9
https://doi.org/10.1007/978-1-4939-3246-7_9