On some Lr-biharmonic Euclidean hypersurfaces

• Autorzy: Mohammadpouri A. , Pashaie F.

Identyfikatory

DOI

10.7862/rf.2016.7

• Języki publikacji: EN

Abstrakty

EN

In decade eighty, Bang-Yen Chen introduced the concept of biharmonic hypersurface in the Euclidean space. An isometrically immersed hypersurface x : Mn → En+1 is said to be biharmonic if ∆2x = 0, where ∆ is the Laplace operator. We study the Lr-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 L0 = ∆. We prove that Lr-biharmonic hypersurface of Lr-finite type and also Lr-biharmonic hypersurface with at most two distinct principal curvatures in Euclidean spaces are r-minimal.

Słowa kluczowe

EN

linearized operator Lr; Lr-biharmonic hypersurfaces; Lr-finite type hypersurfaces; r-minimal; Euclidean space; submanifolds; curvature

PL

hiperprzestrzeń; przestrzeń euklidesowa; podrozmaitość; krzywizna

• Wydawca: Oficyna Wydawnicza Politechniki Rzeszowskiej
• Czasopismo: Journal of Mathematics and Applications
• Rocznik: 2016
• Tom: Vol. 39
• Strony: 91--104
• Opis fizyczny: Bibliogr. 20 poz.

Twórcy

autor

Mohammadpouri A.

• Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran
• Department of Mathematics, Faculty of Basic Sciences, University of Maragheh, P.O.Box 55181-83111, Maragheh, Iran

autor

Pashaie F.

• Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran
• Department of Mathematics, Faculty of Basic Sciences, University of Maragheh, P.O.Box 55181-83111, Maragheh, Iran

Bibliografia

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Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).