On some L1-finite type (hyper)surfaces in {R}^{n+1}
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We say that an isometric immersed hypersurface x : Mn →Rn+1 is of Lk-finite type (Lk-f.t.) if x = Σpi=0 xi for some positive integer p < ∞, xi : M → R^n+1 is smooth and Lkxi = λixiλi ∈ R, 0 ≤ i ≤ p, Lkf = trPk ◦ ∇2f for f ∈ C∞(M), where Pk is the kth Newton transformation, ∇2f is the Hessian of f, Lkx = (Lkx^1,···,Lkx^n+1), x = (x^1,···, x^n+1). In this article we study the following (hyper)surfaces in Rn+1 from the view point of L1-fitniteness type: totally umbilic ones, generalized cylinders S^m(r) × R^n−m, ruled surfaces in R^n+1 and some revolution surfaces in R^3.
Abstract
We say that an isometric immersed hypersurface x : Mn →Rn+1 is of Lk-finite type (Lk-f.t.) if x = Σpi=0 xi for some positive integer p < ∞, xi : M → R^n+1 is smooth and Lkxi = λixiλi ∈ R, 0 ≤ i ≤ p, Lkf = trPk ◦ ∇2f for f ∈ C∞(M), where Pk is the kth Newton transformation, ∇2f is the Hessian of f, Lkx = (Lkx^1,···,Lkx^n+1), x = (x^1,···, x^n+1). In this article we study the following (hyper)surfaces in Rn+1 from the view point of L1-fitniteness type: totally umbilic ones, generalized cylinders S^m(r) × R^n−m, ruled surfaces in R^n+1 and some revolution surfaces in R^3.
참고문헌 (6)
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