Curvature homogeneous hypersurfaces in space forms
Publication
, Journal Article
Bryant, R; Ziller, W; Florit, L
Published in: Advances in Mathematics
May 14, 2025
We provide a classification of curvature homogeneous hypersurfaces in space forms by classifying the ones in and . In higher dimensions, besides the isoparametric and the constant curvature ones, there is a single one in . Besides the obvious examples, we show that there exists an isolated hypersurface with a circle of symmetries and a one parameter family admitting no continuous symmetries. Outside the set of minimal points, which only exists in the case of , every example is, locally and up to covers, of this form.
Duke Scholars
Published In
Advances in Mathematics
DOI
EISSN
1090-2082
ISSN
0001-8708
Publication Date
May 14, 2025
Publisher
Elsevier
Related Subject Headings
- General Mathematics
- 4904 Pure mathematics
- 4902 Mathematical physics
- 4901 Applied mathematics
- 0101 Pure Mathematics
Citation
APA
Chicago
ICMJE
MLA
NLM
Bryant, R., Ziller, W., & Florit, L. (2025). Curvature homogeneous hypersurfaces in space forms. Advances in Mathematics. https://doi.org/10.1016/j.aim.2025.110338
Bryant, Robert, Wolfgang Ziller, and Luis Florit. “Curvature homogeneous hypersurfaces in space forms.” Advances in Mathematics, May 14, 2025. https://doi.org/10.1016/j.aim.2025.110338.
Bryant R, Ziller W, Florit L. Curvature homogeneous hypersurfaces in space forms. Advances in Mathematics. 2025 May 14;
Bryant, Robert, et al. “Curvature homogeneous hypersurfaces in space forms.” Advances in Mathematics, Elsevier, May 2025. Manual, doi:10.1016/j.aim.2025.110338.
Bryant R, Ziller W, Florit L. Curvature homogeneous hypersurfaces in space forms. Advances in Mathematics. Elsevier; 2025 May 14;
Published In
Advances in Mathematics
DOI
EISSN
1090-2082
ISSN
0001-8708
Publication Date
May 14, 2025
Publisher
Elsevier
Related Subject Headings
- General Mathematics
- 4904 Pure mathematics
- 4902 Mathematical physics
- 4901 Applied mathematics
- 0101 Pure Mathematics