Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 42, 2017, 905-920

RIGIDITY THEOREMS FOR MINIMAL SUBMANIFOLDS IN A HYPERBOLIC SPACE

Adriano C. Bezerra and Qiaoling Wang

Universidade de Brasília, Departamento de Matemática, 70910-900, Brasília - DF, Brazil
and Instituto Federal de Educão, Ciência e Tecnologia de Goiás
72811-580, Luziânia - GO, Brazil; adriano.bezerra 'at' ifg.edu.br

Universidade de Brasília, Departamento de Matemática
70910-900, Brasília - DF, Brazil; wang 'at' mat.unb.br

Abstract. Let M be a complete immersed minimal hypersurface in a hyperbolic space. In this paper we establish conditions on the first eigenvalue of the stability and super stability operators and the L^d norm of the length of the second fundamental form of M to imply that M is totally geodesic. Similar results for minimal submanifolds in a hyperbolic space are also proven.

2010 Mathematics Subject Classification: Primary 53C20, 53C42.

Key words: Minimal submanifolds, hyperbolic space, super stability operator.

Reference to this article: A. C. Bezerra and Q. Wang: Rigidity theorems for minimal submanifolds in a hyperbolic space. Ann. Acad. Sci. Fenn. Math. 42 (2017), 905-920.

Full document as PDF file

https://doi.org/10.5186/aasfm.2017.4253