Biharmonic properly immersed submanifolds in Euclidean spaces

被引：56

作者：

Akutagawa, Kazuo ^{[1
]}

Maeta, Shun ^{[1
]}

机构：

[1] Tohoku Univ, GSIS, Div Math, Sendai, Miyagi 9808579, Japan

来源：

GEOMETRIAE DEDICATA | 2013年 / 164卷 / 01期

基金：

日本学术振兴会;

关键词：

Biharmonic map; Biharmonic submanifold; Chen's conjecture; HYPERSURFACES;

D O I：

10.1007/s10711-012-9778-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider a complete biharmonic immersed submanifold M in a Euclidean space . Assume that the immersion is proper, that is, the preimage of every compact set in is also compact in M. Then, we prove that M is minimal. It is considered as an affirmative answer to the global version of Chen's conjecture for biharmonic submanifolds.

引用

页码：351 / 355

页数：5

共 10 条

[1]

[Anonymous], 1998, Kyushu J. Math., DOI DOI 10.2206/KYUSHUJM.52.167

[2]

Chen B. Y, 1988, SOME OPEN PROBLEMS C

[3]

Chen B.-Y., 1991, Memoirs Fac. Sci. Kyushu Univ. Ser. A, Math., V45, P323

[4] MAXIMAL SPACE-LIKE HYPERSURFACES IN LORENTZ-MINKOWSKI SPACES [J].

CHENG, SY ;

YAU, ST .

ANNALS OF MATHEMATICS, 1976, 104 (03) :407-419

[5]

Defever F, 1998, MATH NACHR, V196, P61

[6]

Dimitric I. M., 1992, Bull. Inst. Math. Acad. Sinica, V20, P53

[7] HYPERSURFACES IN E(4) WITH HARMONIC CURVATURE VECTOR FIELD [J].

HASANIS, T ;

VLACHOS, T .

MATHEMATISCHE NACHRICHTEN, 1995, 172 :145-169

[8] Biharmonic Submanifolds in a Riemannian Manifold with Non-Positive Curvature [J].

Nakauchi, Nobumitsu ;

Urakawa, Hajime .

RESULTS IN MATHEMATICS, 2013, 63 (1-2) :467-474

[9] Biharmonic hypersurfaces in a Riemannian manifold with non-positive Ricci curvature [J].

Nakauchi, Nobumitsu ;

Urakawa, Hajime .

ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, 2011, 40 (02) :125-131

[10] HARMONIC-FUNCTIONS ON COMPLETE RIEMANNIAN MANIFOLDS [J].

YAU, ST .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1975, 28 (02) :201-228

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