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In this paper we begin the study of $L_k$-2-type hypersurfaces of a hypersphere $\S^{n+1}\subset\R^{n+2}$ for $k\geq 1$. Let $\psi:\M\rightarrow\S^{4}$ be an orientable $H_k$-hypersurface, which is not an open portion of a hypersphere. Then $\M$ is of $L_k$-2-type if and only if $\M$ is a Clifford tori $\S^1(r_1)\times\S^2(r_2)$, $r_1^2+r_2^2=1$, for appropriate radii, or a tube $T^r(V^2)$ of appropriate constant radius $r$ around the Veronese embedding of the real projective plane $\R P^2(\sqrt3)$.
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참고문헌 (39)
참고문헌 신청
L. J. Alıas / 1992 / Surfaces in the 3-dimensional Lorentz-Minkowski space satisfying x = Ax + B / Pacific J. Math 156(2):201~208
L. J. Alıas / 1992 / Submanifolds in pseudo-Euclidean spaces satisfying the condition x = Ax+B / Geom. Dedicata 42(3):345~354
L. J. Alıas / 1995 / Hypersurfaces in space forms satisfying the condition x = Ax + B / Trans. Amer. Math. Soc 347(5):1793~1801
L. J. Alıas / 2006 / An extension of Takahashi theorem for the linearized operators of the higher order mean curvatures / Geom. Dedicata 121:113~127
L. J. Alıas / 2010 / Hypersurfaces in space forms satisfying the condition Lk = A + b / Taiwanese J. Math 14(5):1957~1978
L. J. Alıas / 1992 / Submanifolds in pseudo-Euclidean spaces satisfying the condition x = Ax+B / Geom. Dedicata 42(3):345~354
L. J. Alıas / 1995 / Hypersurfaces in space forms satisfying the condition x = Ax + B / Trans. Amer. Math. Soc 347(5):1793~1801
L. J. Alıas / 2006 / An extension of Takahashi theorem for the linearized operators of the higher order mean curvatures / Geom. Dedicata 121:113~127
L. J. Alıas / 2010 / Hypersurfaces in space forms satisfying the condition Lk = A + b / Taiwanese J. Math 14(5):1957~1978
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