2024 : 11 : 14
Leila Shahbaz

Leila Shahbaz

Academic rank: Associate Professor
ORCID:
Education: PhD.
ScopusId:
HIndex:
Faculty: 1
Address:
Phone:

Research

Title
On extended biharmonic hypersurfaces with three curvatures
Type
JournalPaper
Keywords
Minkowski space, L_1-biharmonic, isoparametric, 1-minimal.
Year
2023
Journal Proyecciones
DOI
Researchers Firooz Pashaie ، ، Asghar Rahimi ، Leila Shahbaz

Abstract

The subject of harmonic and biharmonic submanifolds, with important role in mathematical physics and differential geometry, arises from the variation problems of ordinary mean curvature vector field. Generally, harmonic submanifolds are biharmonic, but not vice versa. Of course, many examples of biharmonic hypersurfaces are harmonic. A well-known conjecture of Bang-Yen Chen on Euclidean spaces says that every biharmonic submanifold is harmonic. Although the conjecture has not been proven (in general case), it has been affirmed in many cases, and this has led to its spread to various types of submanifolds. Inspired by the conjecture, we study the Lorentz submanifolds of the Lorentz-Minkowski spaces. We consider an advanced version of the conjecture (namely, L_1-conjecture) on Lorentz hypersurfaces of the pseudo-Euclidean 5-space L^5 := E_1^5 (i.e. the Minkowski 5-space). We confirm the extended conjecture on Lorentz hypersurfaces with three principal curvatures.