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Möbius geometry for hypersurfaces in S 4

  • Changping Wang (a1)

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Our purpose in this paper is to study Möbius geometry for those hypersurfaces in S 4 which have different principal curvatures at each point. We will give a complete local Möbius invariant system for such hypersurface in S 4 which determines the hypersurface up to Möbius transformations. And we will classify the so-called Möbius homogeneous hypersurfaces in S 4.

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Copyright

Corresponding author

Nankai Institute of Mathematics, Nankai University, Tianjin, 300071, P. R. China

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Partially supported by the DFG-project “Affine Differential Geometry” at the TU Berlin

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References

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[ 1 ] Blaschke, W., Differentialgeometrie III, Springer-Verlag, Berlin (1929).
[ 2 ] Bryant, R. L., A duality theorem for Willmore surfaces, J. Differential Geom., 20 (1984), 2353.
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[ 6 ] Cecil, T., Lie sphere geometry with application to submanifolds, New York, Springer 1992.
[ 7 ] Miyaoka, R., Compact Dupin hypersurfaces with three principal curvatures, Math. Z., 187(1984), 433452.
[ 8 ] Münzner, H. F., Isoparametrische Hyperflächen in Sphären, Math. Ann., 251 (1980), 5771.
[ 9 ] Pinkall, U., Dupin’sche Hyperflächen, Manuscripta Math., 51 (1985), 89119.
[10] Pinkall, U., Dupin hypersurfaces, Math. Ann., 270 (1985), 427440.
[11] Wang, C. P., Surfaces in Möbius geometry, Nagoya Math. J., 125 (1992), 5372.
[12] Warner, F. W., Fundations of differentiable manifolds and Lie group, New York, Springer 1983.
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Möbius geometry for hypersurfaces in S 4

  • Changping Wang (a1)

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