SCALAR CURVATURE OF HYPERSURFACES WITH CONSTANT MEAN CURVATURE IN SPHERES

ZHANG, QIN

Glasgow mathematical journal, Tome 54 (2012) no. 1, pp. 67-75

Résumé

Let Mn be an n-dimensional closed hypersurface with constant mean curvature H satisfying |H| ≤ ε(n) in a unit sphere Sn+1(1), n ≤ 8 and S the square of the length of the second fundamental form of M. There exists a constant δ(n, H) > 0, which depends only on n and H such that if S0 ≤ S ≤ S0 + δ(n, H), then S ≡ S0 and M is isometric to a Clifford hypersurface, where ε(n) is a sufficiently small constant depending on n and .

Détail

DOI : 10.1017/S0017089511000358

Mots-clés : Primary 53C42, 53B25

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