p -调和态射的构造

数学物理学报

p -调和态射的构造

黄利兵;莫小欢

北京大学数学科学学院北京 100871

收稿日期:2005-05-11 修回日期:2007-06-28 出版日期:2008-04-25 发布日期:2008-04-25
通讯作者: 莫小欢
基金资助:
国家自然科学基金(10471001)资助

On the Construction of {\boldmath $p$}-harmonic Morphisms

LibingHuang ; Mo Xiaohuan

School of Mathematical Sciences, Peking University, Beijing 100871

Received:2005-05-11 Revised:2007-06-28 Online:2008-04-25 Published:2008-04-25
Contact: Mo Xiaohuan

摘要/Abstract

摘要： 该文通过考虑水平共形淹没中的度量形变所产生的$p$ -张力场的变化规律, 构造了新的$p$ -调和态射. 特别地, 作者解析构造了新的$10/3$ -调和态射$\phi:R^4\backslash\{0\}\to{R^3}$, 其中$R^4\backslash\{0\}$和$R^3$都取标准的欧氏度量. 最后作者用纤维是1维的主丛给出了$p$ -调和态射的整体刻画.

关键词: p -调和态射, 水平共形淹没, 主丛.

Abstract: In this note the authors construct new $p$-harmonic morphisms by studying the $p$-tension field under changes of metrics for horizontally conformal submersions. In particular, the authors explicitly construct new $\frac{10}{3}$-harmonic morphism $\phi:R^4\setminus \{0\}\rightarrow R^3$ with respect to standard Euclidean metrics. Finally the authors characterize $p$-harmonic morphisms with one dimensional fibres (globally) in terms of principal bundles.

Key words: $p$-harmonic morphism, Horizontally conformal submersion, Principal bundle

黄利兵;莫小欢. p -调和态射的构造[J]. 数学物理学报, 2008, 28(2): 232-239.

LibingHuang ; Mo Xiaohuan. On the Construction of {\boldmath $p$}-harmonic Morphisms[J]. Acta mathematica scientia,Series A, 2008, 28(2): 232-239.