- Tytuł:
- On some Lr-biharmonic Euclidean hypersurfaces
- Autorzy:
-
Mohammadpouri, A.
Pashaie, F. - Powiązania:
- https://bibliotekanauki.pl/articles/357780.pdf
- Data publikacji:
- 2016
- Wydawca:
- Politechnika Rzeszowska im. Ignacego Łukasiewicza. Oficyna Wydawnicza
- Tematy:
-
linearized operator Lr
Lr-biharmonic hypersurfaces
Lr-finite type hypersurfaces
r-minimal
Euclidean space
submanifolds
curvature
hiperprzestrzeń
przestrzeń euklidesowa
podrozmaitość
krzywizna - Opis:
- In decade eighty, Bang-Yen Chen introduced the concept of biharmonic hypersurface in the Euclidean space. An isometrically immersed hypersurface $x : M^{n} \rightarrow \mathbb{E}^{n+1}$ is said to be biharmonic if $\Delta^{2}x = 0$, where $\Delta$ is the Laplace operator. We study the $L_{r}$-biharmonic hypersurfaces as a generalization of biharmonic ones, where Lr is the linearized operator of the $(r + 1)$th mean curvature of the hypersurface and in special case we have $L_{0} = \Delta$. We prove that $L_{r}$-biharmonic hypersurface of $L_{r}$-finite type and also $L_{r}$-biharmonic hypersurface with at most two distinct principal curvatures in Euclidean spaces are r-minimal.
- Źródło:
-
Journal of Mathematics and Applications; 2016, 39; 91-104
1733-6775
2300-9926 - Pojawia się w:
- Journal of Mathematics and Applications
- Dostawca treści:
- Biblioteka Nauki
Artykuł