调和态射与Jacobi场的扭结构
Twistorial constructions of harmonic morphisms and Jacobi fields
摘要：
扭量方法在调和映射和调和态射的研究中提供了一个强有力的工具。事实上，他们的使用使我们能够产生各种例子的调和态射定义的4维流形，并在某些情况下，一个完整的分类。在本工作的第一部分中，我们推广了这些结构，以获得从高维流形的调和态射。扭量方法在雅可比场研究中的应用已被证明是卓有成效的，产生了一系列结果。在这项工作的第二部分中，我们给出了一个一般的治疗Jacobi字段和变化的扭量空间之间的关系，获得一阶类似的twistorial结构。
英文摘要：
Twistor methods provide a powerful tool in the study of harmonic maps and harmonic morphisms. Indeed, their use has enabled us to produce a variety of examples of harmonic morphisms defined on 4-dimensional manifolds, and a complete classification in some cases. In the first part of this work, we generalize those constructions to obtain harmonic morphisms from higher-dimensional manifolds. The use of twistor methods in the study of Jacobi fields has proved quite fruitful, leading to a series of results. In the second part of this work we give a general treatment of the relations between Jacobi fields and variations in the twistor space, obtaining first-order analogues of twistorial constructions.
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