Compact minimal hypersurfaces with index one in the real projective space |
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| Authors: | M do Carmo M Ritoré and A Ros |
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| Institution: | (1) Instituto de Matematica Pura e Aplicada, Estrada Dona Castorina, Rio de Janeiro, Brasil, e-mail: manfredo@impa.br, BR;(2) Departamento de Geometría y Topología, Universidad de Granada, E-18071 Granada, Espa?a, e-mail: ritore@ugr.es, and aros@ugr.es, BR |
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| Abstract: | Let M
n
be a compact (two-sided) minimal hypersurface in a Riemannian manifold . It is a simple fact that if has positive Ricci curvature then M cannot be stable (i.e. its Jacobi operator L has index at least one). If is the unit sphere and L has index one, then it is known that M must be a totally geodesic equator.?We prove that if is the real projective space , obtained as a metric quotient of the unit sphere, and the Jacobi operator of M has index one, then M is either a totally geodesic sphere or the quotient to the projective space of the hypersurface obtained as the product of two spheres of dimensions n
1, n
2 and radius R
1, R
2, with and .
Received: June 6, 1998 |
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| Keywords: | |
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