Generalized harmonic morphisms and horizontally weakly conformal biharmonic maps
Generalized harmonic morphisms and horizontally weakly conformal biharmonic maps
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广义调和态射和水平弱共形双调和映射
DOI：
10.1016/j.jmaa.2018.04.044
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发表时间：
2017
影响因子：
1.3
通讯作者：
Ye
中科院分区：
文献类型：
--
作者：
Elsa Ghandour;Ye
调和态射是黎曼流形之间的映射，它将调和函数拉回调和函数。这些图的特点是水平弱共形谐波图，它们在数学的几个领域有许多有趣的联系和应用（详见Baird和Wood的书[2]）。本文研究了广义调和态射，它被定义为将调和函数拉回到双调和函数的黎曼流形之间的映射。我们得到了欧几里得空间中广义调和态射的一些刻画，并给出了两种构造方法，这两种构造方法可以产生许多非调和态射的广义调和态射的例子。我们还给出了在弯曲积空间的投影之间的广义调和态射的完全分类，给出了无限多的弯曲积流形上的适当双调和黎曼淹没和保形淹没的例子。
Harmonic morphisms are maps between Riemannian manifolds that pull back harmonic functions to harmonic functions. These maps are characterized as horizontally weakly conformal harmonic maps and they have many interesting links and applications to several areas in mathematics (see the book [2] by Baird and Wood for details). In this paper, we study generalized harmonic morphisms which are defined to be maps between Riemannian manifolds that pull back harmonic functions to biharmonic functions. We obtain some characterizations of generalized harmonic morphisms into a Euclidean space and give two methods of constructions that can be used to produce many examples of generalized harmonic morphisms which are not harmonic morphisms. We also give a complete classification of generalized harmonic morphisms among the projections of a warped product space, which provides infinitely many examples of proper biharmonic Riemannian submersions and conformal submersions from a warped product manifold.