Rigidity of minimal hypersurfaces of spheres with constant ricci curvature

• Autores: Oscar Mario Perdomo
• Localización: Revista Colombiana de Matemáticas, ISSN-e 0034-7426, Vol. 38, Nº. 2, 2004, págs. 73-85
• Idioma: inglés
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• Resumen

  • Let M be a compact oriented minimal hypersurface of the unit ndimensional sphere Sn. In this paper we will point out that if the Ricci curvature of M is constant, then, we have that either Ric t^ 1 and M is isometric to an equator or, n is odd, Ric t^ n-3n-2 and M is isometric to S n-12 ( p2 2 ) * S n-12 ( p2 2 ).Next, we will prove that there exists a positive number s^(n) such that if the Ricci curvature of a minimal hypersurface immersed by first eigenfunctions M satisfies that n-3n-2 - s^(n) <= Ric <= n-3n-2 + s^(n) and the average of the scalar curvature is n-3n-2 , then, the ricci curvature of M must be constant and therefore M must be isometric to S n-12 ( p2 2 ) * S n-12 ( p2 2 ).