HYPERSURFACES WITH CONSTANT k-TH MEAN CURVATURE IN A LORENTZIAN SPACE FORM
نویسندگان
چکیده
In this paper, we study n(n ≥ 3)-dimensional complete connected and oriented space-like hypersurfaces Mn in an (n+1)-dimensional Lorentzian space form Mn+1 1 (c) with non-zero constant k-th (k < n) mean curvature and two distinct principal curvatures λ and μ. We give some characterizations of Riemannian product H(c1) ×Mn−m(c2) and show that the Riemannian product Hm(c1)×Mn−m(c2) is the only complete connected and oriented space-like hypersurface inMn+1 1 (c) with constant k-th mean curvature and two distinct principal curvatures, if the multiplicities of both principal curvatures are greater than 1, or if the multiplicity of λ is n − 1, lim s→±∞ λk 6= Hk and the sectional curvature of Mn is non-negative (or non-positive) when c > 0, non-positive when c ≤ 0, where Mn−m(c2) denotes Rn−m, Sn−m(c2) or Hn−m(c2), according to c = 0, c > 0 or c < 0, where s is the arc length of the integral curve of the principal vector field corresponding to the principal curvature μ.
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