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SOME CLASSIFICATIONS OF LORENTZIAN SURFACES WITH FINITE TYPE GAUSS MAP IN THE MINKOWSKI 4-SPACE
- Part of
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- Journal:
- Journal of the Australian Mathematical Society / Volume 99 / Issue 3 / December 2015
- Published online by Cambridge University Press:
- 13 August 2015, pp. 415-427
- Print publication:
- December 2015
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- Article
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SCALAR CURVATURE OF HYPERSURFACES WITH CONSTANT MEAN CURVATURE IN A SPHERE
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- Journal:
- Glasgow Mathematical Journal / Volume 51 / Issue 2 / May 2009
- Published online by Cambridge University Press:
- 01 May 2009, pp. 413-423
- Print publication:
- May 2009
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- Article
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Let M be an n-dimensional closed hypersurface with constant mean curvature H satisfying |H| ≤ ϵ(n) in a unit sphere Sn+1, n ≤ 7, 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
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