Supplement on curved flats in the space of point pairs and isothermic surfaces: A quaternionic calculus
Supplement on curved flats in the space of point pairs and isothermic surfaces: A quaternionic calculus
复制标题
点对和等温曲面空间中曲面平面的补充：四元数微积分
DOI：
10.4171/dm/33
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发表时间：
1997
影响因子：
0.9
通讯作者：
U. Hertrich
中科院分区：
文献类型：
--
作者：
U. Hertrich
阐述了共形4-球面中曲面对的四元数演算。这种演算，然后用来讨论在对称空间的点对和达布和Christoffel对等温表面的曲面之间的关系。对某些空间形式中常平均曲率曲面之间的关系提出了一种新的观点，特别是给出了3-双曲空间中常平均曲率为1的曲面的Bryant Weierstrass型表示的一种新形式.
A quaternionic calculus for surface pairs in the conformal 4-sphere is elaborated. This calculus is then used to discuss the relation between curved flats in the symmetric space of point pairs and Darboux and Christoffel pairs of isothermic surfaces. A new viewpoint on relations between surfaces of constant mean curvature in certain space forms is presented --- in particular, a new form of Bryant's Weierstrass type representation for surfaces of constant mean curvature 1 in hyperbolic 3-space is given.