First eigenvalue of submanifolds in Euclidean space.
Cai, Kairen (2000)
International Journal of Mathematics and Mathematical Sciences
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Cai, Kairen (2000)
International Journal of Mathematics and Mathematical Sciences
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Franki Dillen, Johan Fastenakels, Stefan Haesen, Joeri Van der Veken, Leopold Verstraelen (2013)
Kragujevac Journal of Mathematics
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Publications de l'Institut Mathématique
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Mehmet Bektaş, Mahmut Ergüt (1999)
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J. Deprez, R. Deszcz, L. Verstraelen (1988)
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Liu, Ximin (1999)
International Journal of Mathematics and Mathematical Sciences
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Qiaoling Wang, Chang Yu Xia (2007)
Czechoslovak Mathematical Journal
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In this paper we study the topological and metric rigidity of hypersurfaces in , the -dimensional hyperbolic space of sectional curvature . We find conditions to ensure a complete connected oriented hypersurface in to be diffeomorphic to a Euclidean sphere. We also give sufficient conditions for a complete connected oriented closed hypersurface with constant norm of the second fundamental form to be totally umbilic.