Let Mn(n≥2) be an immersed umbilic-free hypersurface in the(n+1)-dimensional unit sphere Sn+1. Then Mn is associated witha so-called M(o)bius metric g, and a M(o)bius second fundamental form Bwhich are invariants of ...Let Mn(n≥2) be an immersed umbilic-free hypersurface in the(n+1)-dimensional unit sphere Sn+1. Then Mn is associated witha so-called M(o)bius metric g, and a M(o)bius second fundamental form Bwhich are invariants of Mn under the M(o)bius transformation groupof Sn+1.In this paper, we classify all umbilic-free hypersurfaces withparallel M(o)bius second fundamental form.展开更多
An umbilic-free hypersurface in the unit sphere is called MSbius isoparametric if it satisfies two conditions, namely, it has vanishing MSbius form and has constant MSbius principal curvatures. In this paper, under th...An umbilic-free hypersurface in the unit sphere is called MSbius isoparametric if it satisfies two conditions, namely, it has vanishing MSbius form and has constant MSbius principal curvatures. In this paper, under the condition of having constant MSbius principal curvatures, we show that the hypersurface is of vanishing MSbius form if and only if its MSbius form is parallel with respect to the Levi-Civita connection of its MSbius metric. Moreover, typical examples are constructed to show that the condition of having constant MSbius principal curvatures and that of having vanishing MSbius form are independent of each other.展开更多
An immersed umbilic-free submanifold in the unit sphere is called Blaschke isoparametric if its Mbius form vanishes identically and all of its Blaschke eigenvalues are constant. In this paper,we give a complete classi...An immersed umbilic-free submanifold in the unit sphere is called Blaschke isoparametric if its Mbius form vanishes identically and all of its Blaschke eigenvalues are constant. In this paper,we give a complete classification for all Blaschke isoparametric hypersurfaces with three distinct Blaschke eigenvalues.展开更多
基金The First author is partially supported by grants of CSC,the National Natural Science Foundation of ChinaOutstanding Youth Foundation of Henan,Chinathe second author is partially Supported by the Alexander von Humboldt Stiftung,grant of Tsinghua University and Zhongdian grant of NSFC.
文摘Let Mn(n≥2) be an immersed umbilic-free hypersurface in the(n+1)-dimensional unit sphere Sn+1. Then Mn is associated witha so-called M(o)bius metric g, and a M(o)bius second fundamental form Bwhich are invariants of Mn under the M(o)bius transformation groupof Sn+1.In this paper, we classify all umbilic-free hypersurfaces withparallel M(o)bius second fundamental form.
基金Supported by National Natural Science Foundation of China (Grant No.10671181)
文摘An umbilic-free hypersurface in the unit sphere is called MSbius isoparametric if it satisfies two conditions, namely, it has vanishing MSbius form and has constant MSbius principal curvatures. In this paper, under the condition of having constant MSbius principal curvatures, we show that the hypersurface is of vanishing MSbius form if and only if its MSbius form is parallel with respect to the Levi-Civita connection of its MSbius metric. Moreover, typical examples are constructed to show that the condition of having constant MSbius principal curvatures and that of having vanishing MSbius form are independent of each other.
基金supported by National Natural Science Foundation of China (Grant Nos. 10671181, 11071225)
文摘An immersed umbilic-free submanifold in the unit sphere is called Blaschke isoparametric if its Mbius form vanishes identically and all of its Blaschke eigenvalues are constant. In this paper,we give a complete classification for all Blaschke isoparametric hypersurfaces with three distinct Blaschke eigenvalues.
