Abstract

It is our purpose to study curvature structures of compact hypersurfaces in the unit sphere Sⁿ⁺¹(1). We proved that the Riemannian product S¹() ×Sⁿ⁻¹(c) is the only compact hypersurfaces in Sⁿ⁺¹(1) with infinite fundamental group, which satisfy r ≥ and S ≤ (n − 1) + , where n(n − 1)r is the scalar curvature of hypersurfaces and c² = . In particular, we obtained that the Riemannian product S¹() × Sⁿ⁻¹(c) is the only compact hypersurfaces with infinite fundamental group in Sⁿ⁺¹(1) if the sectional curvatures are nonnegative.

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