A Note on Gap Theorems for Complete λ-Hypersurfaces

A Note on Gap Theorems for Complete λ-Hypersurfaces

In this paper, we prove some gap theorems for complete λ -hypersurfaces. Assume that the L n / 2 -norm of a quantity concerning the trace-free second fundamental form and the mean curvature is finite, we show that the hypersurface must be a plane. The same results for λ -surfaces in R 3 also given p...

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Veröffentlicht in:Mediterranean journal of mathematics 2023-02, Vol.20 (1), Article 4
Hauptverfasser: Dung, Nguyen Thac, Duc, Nguyen Van
Format: Artikel
Sprache:eng
Schlagworte:
Curvature
Hyperspaces
Mathematics
Mathematics and Statistics
Theorems
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Zusammenfassung:In this paper, we prove some gap theorems for complete λ -hypersurfaces. Assume that the L n / 2 -norm of a quantity concerning the trace-free second fundamental form and the mean curvature is finite, we show that the hypersurface must be a plane. The same results for λ -surfaces in R 3 also given provided L 4 -curvature pinching conditions.
ISSN:1660-5446
1660-5454
DOI:10.1007/s00009-022-02208-x