HYPERSURFACES IN S-4 THAT ARE OF L-k-2-TYPE

作者：Lucas Pascual^*; Ramirez Ospina Hector Fabian

来源：Bulletin of the Korean Mathematical Society, 2016, 53(3): 885-902.

DOI：10.4134/BKMS.b150401

• linearized operator L-k
• L-k-finite-type hypersurface
• higher order mean curvatures
• Newton transformations

In this paper we begin the study of L-k-2-type hypersurfaces of a hypersphere S-n (vertical bar 1) subset of R-n vertical bar 2 for k >= 1. Let psi : M-3 -> S-4 be an orientable H-k-hypersurface, which is not an open portion of a hypersphere. Then M-3 is of L-k-2-type if and only if M-3 is a Clifford tori S-1 (r(1)) x S-2 (r(2)), r(1)(2) = r(2)(2) = 1, for appropriate radii, or a tube T-r (V-2) of appropriate constant radius r around the Veronese embedding of the real projective plane RP2(root 3).

• 出版日期2016-5