On Chen's biharmonic conjecture for hypersurfaces in R5

被引：20

作者：

Fu, Yu ^{[1
]}

Hong, Min-Chun ^{[2
]}

Zhan, Xin ^{[3
]}

机构：

[1] Dongbei Univ Finance & Econ, Sch Data Sci & Artificial Intelligence, Dalian 116025, Peoples R China

[2] Univ Queensland, Dept Math, Brisbane, Qld 4072, Australia

[3] Dalian Univ Technol, Sch Math Sci, Dalian 116023, Peoples R China

来源：

ADVANCES IN MATHEMATICS | 2021年 / 383卷

基金：

澳大利亚研究理事会;

关键词：

Biharmonic maps; Biharmonic submanifolds; Chen's conjecture; SUBMANIFOLDS; CURVATURE; SURFACES;

D O I：

10.1016/j.aim.2021.107697

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A longstanding conjecture on biharmonic submanifolds, proposed by Chen in 1991, is that any biharmonic submanifold in a Euclidean space is minimal. In the case of a hypersurface M-n in Rn+1, Chen's conjecture was settled in the case of n = 2 by Chen and Jiang around 1987 independently. Hasanis and Vlachos in 1995 settled Chen's conjecture for a hypersurface with n = 3. However, the general Chen's conjecture on a hypersurface M-n remains open for n > 3. In this paper, we settle Chen's conjecture for hypersurfaces in R-5 for n = 4. (C) 2021 Elsevier Inc. All rights reserved.

引用

页数：28

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