** Authors:**
SHICHANG SHU, SANYANG LIU

** Abstract: **
Let M^n be an n\(n \geq 3)-dimensional complete connected
and oriented hypersurface in M^{n+1}(c)(c \geq 0) with constant mean
curvature H and with two distinct principal curvatures, one of which
is simple. We show that (1) if c=1 and the squared norm of the second
fundamental form of M^n satisfies a rigidity condition (1.3), then M^n
is isometric to the Riemannian product S^1(\sqrt{1-a^2}) \times
S^{n-1}(a); (2) if c=0, H \neq 0 and the squared norm of the second
fundamental form of M^n satisfies S \geq n^2H^2/(n-1), then M^n is
isometric to the Riemannian product S^{n-1}(a)\times R or S^1(a) \times
R^{n-1}

** Keywords: **
Hypersurface, scalar curvature, mean curvature, principal curvature

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