A gap theorem for hypersurfaces of the sphere with constant scalar curvature one |
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| Authors: | H Alencar M do Carmo W Santos |
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| Institution: | 1.Universidade Federal de Alagoas, Departamento de Matemática, 57072-900 Maceió - AL, Brazil? e-mail: hilario@mat.ufal.br,BR;2.Instituto de Matemática Pura e Aplicada (IMPA), Estrada Dona Castorina 110, 22460-320 Rio de Janeiro - RJ, Brazil? e-mail: manfredo@impa.br,BR;3.Universidade Federal do Rio de Janeiro, Departamento de Matemática, Caixa Postal 68530, 21945-970 Rio de Janeiro - RJ, Brazil? e-mail: walcy@im.ufrj.br,BR |
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| 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.
Received: October 12, 2001 |
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| Keywords: | , Scalar curvature, sphere, Clifford torus, index one, projective space, |
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