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In this paper we begin the study of Lk-2-type hypersurfaces of a hypersphere S n+1  R n+2 for k  1. Let : M 3 ! S 4 be an ori- entable Hk-hypersurface, which is not an open portion of a hypersphere. ThenM3 is ofLk-2-type if and only ifM3 is a Clifford tori S1(r1)×S2(r2), r2 +r 2 = 1, for appropriate radii, or a tube T r(V 2) of appropriate con- stant radiusr around the Veronese embedding of the real projective plane RP 2( p 3).

HYPERSURFACES IN 𝕊4THAT ARE OF Lk-2-TYPE

HYPERSURFACES IN 𝕊⁴THAT ARE OF L_k-2-TYPE