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학술연구/단체지원/교육 등 연구자 활동을 지속하도록 DBpia가 지원하고 있어요.
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Consider a hypersurface $M^n$ in $\mathbb{R}^{n+1}$ with $n$ distinct principal curvatures, parametrized by lines of curvature with vanishing Laplace invariants. (1) If the lines of curvature are planar, then there are no such hypersurfaces for $n{\geq}4$, and for $n=3$, they are, up to M$\ddot{o}$bius transformations Dupin hypersurfaces with constant M$\ddot{o}$bius curvature. (2) If the principal curvatures are given by a sum of functions of separated variables, there are no such hypersurfaces for $n{\geq}4$, and for $n=3$, they are, up to M$\ddot{o}$bius transformations, Dupin hypersurfaces with constant M$\ddot{o}$bius curvature.
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참고문헌 (11)
참고문헌 신청
C. M. C. Riveros / 2005 / Dupin hypersurfaces in R5 / Canad. J. Math 57 (6) : 1291 ~ 1313
C. M. C. Riveros / 2008 / On Dupin hypersurfaces with constant Mobius curvature / Pacific J. Math 236 (1) : 89 ~ 103
N. Kamran / 1996 / Laplace transformation in higher dimensions / Duke Math. J 84 (1) : 237 ~ 266
N. Kamran / 1998 / Periodic systems for the higher-dimensional Laplace transformation / Discrete Contin. Dynam. Systems 4 (2) : 359 ~ 378
R. Miyaoka / 1989 / Dupin hypersurfaces and a Lie invariant / Kodai Math. J 12 (2) : 228 ~ 256
C. M. C. Riveros / 2008 / On Dupin hypersurfaces with constant Mobius curvature / Pacific J. Math 236 (1) : 89 ~ 103
N. Kamran / 1996 / Laplace transformation in higher dimensions / Duke Math. J 84 (1) : 237 ~ 266
N. Kamran / 1998 / Periodic systems for the higher-dimensional Laplace transformation / Discrete Contin. Dynam. Systems 4 (2) : 359 ~ 378
R. Miyaoka / 1989 / Dupin hypersurfaces and a Lie invariant / Kodai Math. J 12 (2) : 228 ~ 256
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