Biharmonic Hypersurfaces in Pseudo-Riemannian Space Forms with at Most Two Distinct Principal Curvatures
In this paper, we show that biharmonic hypersurfaces with at most two distinct principal curvatures in pseudo-Riemannian space form Nsn+1c with constant sectional curvature c and index s have constant mean curvature. Furthermore, we find that such biharmonic hypersurfaces Mr2k−1 in even-dimensional...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2020-01-01
|
| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2020/2182975 |
| id |
doaj-3b964a9c445148a0a17e47d5f9c5d484 |
|---|---|
| record_format |
Article |
| spelling |
doaj-3b964a9c445148a0a17e47d5f9c5d4842020-11-25T03:13:21ZengHindawi LimitedJournal of Function Spaces2314-88962314-88882020-01-01202010.1155/2020/21829752182975Biharmonic Hypersurfaces in Pseudo-Riemannian Space Forms with at Most Two Distinct Principal CurvaturesChao Yang0Jiancheng Liu1College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, ChinaCollege of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, ChinaIn this paper, we show that biharmonic hypersurfaces with at most two distinct principal curvatures in pseudo-Riemannian space form Nsn+1c with constant sectional curvature c and index s have constant mean curvature. Furthermore, we find that such biharmonic hypersurfaces Mr2k−1 in even-dimensional pseudo-Euclidean space Es2k, Ms−12k−1 in even-dimensional de Sitter space Ss2kcc>0, and Ms2k−1 in even-dimensional anti-de Sitter space ℍs2kcc<0 are minimal.http://dx.doi.org/10.1155/2020/2182975 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Chao Yang Jiancheng Liu |
| spellingShingle |
Chao Yang Jiancheng Liu Biharmonic Hypersurfaces in Pseudo-Riemannian Space Forms with at Most Two Distinct Principal Curvatures Journal of Function Spaces |
| author_facet |
Chao Yang Jiancheng Liu |
| author_sort |
Chao Yang |
| title |
Biharmonic Hypersurfaces in Pseudo-Riemannian Space Forms with at Most Two Distinct Principal Curvatures |
| title_short |
Biharmonic Hypersurfaces in Pseudo-Riemannian Space Forms with at Most Two Distinct Principal Curvatures |
| title_full |
Biharmonic Hypersurfaces in Pseudo-Riemannian Space Forms with at Most Two Distinct Principal Curvatures |
| title_fullStr |
Biharmonic Hypersurfaces in Pseudo-Riemannian Space Forms with at Most Two Distinct Principal Curvatures |
| title_full_unstemmed |
Biharmonic Hypersurfaces in Pseudo-Riemannian Space Forms with at Most Two Distinct Principal Curvatures |
| title_sort |
biharmonic hypersurfaces in pseudo-riemannian space forms with at most two distinct principal curvatures |
| publisher |
Hindawi Limited |
| series |
Journal of Function Spaces |
| issn |
2314-8896 2314-8888 |
| publishDate |
2020-01-01 |
| description |
In this paper, we show that biharmonic hypersurfaces with at most two distinct principal curvatures in pseudo-Riemannian space form Nsn+1c with constant sectional curvature c and index s have constant mean curvature. Furthermore, we find that such biharmonic hypersurfaces Mr2k−1 in even-dimensional pseudo-Euclidean space Es2k, Ms−12k−1 in even-dimensional de Sitter space Ss2kcc>0, and Ms2k−1 in even-dimensional anti-de Sitter space ℍs2kcc<0 are minimal. |
| url |
http://dx.doi.org/10.1155/2020/2182975 |
| work_keys_str_mv |
AT chaoyang biharmonichypersurfacesinpseudoriemannianspaceformswithatmosttwodistinctprincipalcurvatures AT jianchengliu biharmonichypersurfacesinpseudoriemannianspaceformswithatmosttwodistinctprincipalcurvatures |
| _version_ |
1715274542718386176 |