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On a characterization of round spheres
Leyla Onat 대한수학회 2002 대한수학회보 Vol.39 No.4
It is shown that, an immersion of n-dimensional compact manifold withoutboundary into left( n+1right) -dimensional Euclidean space, hyperbolicspace or the open half spheres, is a totally umbilic immersion if for some %r, r=2,3,cdots,n the r-th mean curvature H_{r} does notvanish and there are nonnegative constantsC_{1},C_{2},cdots,C_{r} such thatbegin{equation*}H_{r}=sum_{i=1}^{r-1}C_{i}H_{i}.end{equation*}
ON A CHARACTERIZATION OF ROUND SPHERES
Onat, Leyla Korean Mathematical Society 2002 대한수학회보 Vol.39 No.4
It is shown that, an immersion of n-dimensional compact manifold without boundary into (n + 1)-dimensional Euclidean space, hyperbolic space or the open half spheres, is a totally umbilic immersion if for some r, r =2, 3, …, n the r-th mean curvature Hr does not vanish and there are nonnegative constants $C_1$, $C_2$, …, $C_{r}$ such that (equation omitted)d)