Constant mean curvature hypersurfaces with two principal curvatures in a sphere |
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Authors: | Yu-Chung Chang |
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Institution: | (1) Department of Finance, Hsing Wu College, Linkou, Taiwan |
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Abstract: | In this paper we consider a compact oriented hypersurface M
n
with constant mean curvature H and two distinct principal curvatures λ and μ with multiplicities (n − m) and m, respectively, immersed in the unit sphere S
n+1. Denote by the trace free part of the second fundamental form of M
n
, and Φ be the square of the length of . We obtain two integral formulas by using Φ and the polynomial . Assume that B
H,m
is the square of the positive root of P
H,m
(x) = 0. We show that if M
n
is a compact oriented hypersurface immersed in the sphere S
n+1 with constant mean curvatures H having two distinct principal curvatures λ and μ then either or . In particular, M
n
is the hypersurface .
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Keywords: | Constant mean curvature Principal curvatures Hypersurface Sphere |
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