Rigidity properties of p-biharmonic maps and p-biharmonic submanifolds

被引：1

作者：

Barker, W. ^{[1
]}

Dung, N. T. ^{[2
]}

Seo, K. ^{[3
]}

Tuyen, N. D. ^{[4
]}

机构：

[1] Univ Arkansas, Dept Math & Stat, Little Rock, AR 72204 USA

[2] Vietnam Natl Univ, Univ Sci, Fac Math Mech Informat, Hanoi, Vietnam

[3] Sookmyung Womens Univ, Dept Math, Cheongpa Ro 47 Gil 100, Seoul 04310, South Korea

[4] Hanoi Univ Civil Engn, Dept Math, Hanoi, Vietnam

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2024年 / 537卷 / 02期

基金：

新加坡国家研究基金会;

关键词：

p-Biharmonic maps; p-Biharmonic submanifolds; Chen's conjecture; Minimal submanifolds; IMMERSED SUBMANIFOLDS; HYPERSURFACES;

D O I：

10.1016/j.jmaa.2024.128310

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We give some rigidity properties of a p-biharmonic map u :(M, g) -> (N, h) between Riemannian manifolds (M-n, g) and (N-m, h). We first provide various sufficient conditions for p-biharmonic maps to be harmonic. Moreover, when the map u is an isometric immersion, by assuming that the L-n/2-norm of the sectional curvature on M is sufficiently small or if the fundamental tone of the p-biharmonic submanifold is sufficiently big, it is proved that M is minimal. (c) 2024 Elsevier Inc. All rights reserved.

引用

页数：18

共 32 条

[1] Biharmonic properly immersed submanifolds in Euclidean spaces [J].

Akutagawa, Kazuo ;

Maeta, Shun .

GEOMETRIAE DEDICATA, 2013, 164 (01) :351-355

[2] Biharmonic hypersurfaces in 4-dimensional space forms [J].

Balmus, Adina ;

Montaldo, Stefano ;

Oniciuc, Cezar .

MATHEMATISCHE NACHRICHTEN, 2010, 283 (12) :1696-1705

[3]

Besse ArthurL., 1987, ERGEBNISSE MATH IHRE, V10

[4] Biharmonic submanifolds of S3 [J].

Caddeo, R ;

Montaldo, S ;

Oniciuc, C .

INTERNATIONAL JOURNAL OF MATHEMATICS, 2001, 12 (08) :867-876

[5] Biharmonic submanifolds in spheres [J].

Caddeo, R ;

Montaldo, S ;

Oniciuc, C .

ISRAEL JOURNAL OF MATHEMATICS, 2002, 130 (1) :109-123

[6]

Caddeo R., 2001, Contemp. Math., V288, P286

[7] ON p-BIHARMONIC SUBMANIFOLDS IN NONPOSITIVELY CURVED MANIFOLDS [J].

Cao, Xiangzhi ;

Luo, Yong .

KODAI MATHEMATICAL JOURNAL, 2016, 39 (03) :567-578

[8]

Chen B.Y., 1991, Soochow J. Math, V17, P169

[9]

Chen B.Y., 1996, SOOCHOW J MATH, V22, P117

[10] Biharmonic ideal hypersurfaces in Euclidean spaces [J].

Chen, Bang-Yen ;

Munteanu, Marian Ioan .

DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, 2013, 31 (01) :1-16

← 1 2 3 4 →