Abstract.
We consider closed hypersurfaces of the sphere with scalar curvature one, prove a gap theorem for a modified second fundamental form and determine the hypersurfaces that are at the end points of the gap. As an application we characterize the closed, two-sided index one hypersurfaces with scalar curvature one in the real projective space.
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Received: October 12, 2001
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Alencar, H., do Carmo, M. & Santos, W. A gap theorem for hypersurfaces of the sphere with constant scalar curvature one. Comment. Math. Helv. 77, 549–562 (2002). https://doi.org/10.1007/s00014-002-8351-1
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DOI: https://doi.org/10.1007/s00014-002-8351-1