具有球对称度量的矢量束的调和截面

IF 0.5 4区数学 Q3 MATHEMATICS

Advances in Geometry Pub Date : 2022-01-01 DOI:10.1515/advgeom-2021-0030

M. Abbassi, Ibrahim Lakrini

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引用次数: 1

摘要

摘要:我们在黎曼流形上赋予一个具有纤维度规和相容连接的任意向量束，并赋予一个球对称度规(参见[4])，我们首先研究了其截面的光滑映射的调和性，然后研究了通过光滑截面变化的能量泛函的临界点。我们还描述了垂直谐波部分。最后，我们给出了一些特殊向量束的例子，在某些情况下恢复了一些经典的调和性结果。

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Harmonic sections of vector bundles with spherically symmetric metrics

Abstract We equip an arbitrary vector bundle over a Riemannian manifold, endowed with a fiber metric and a compatible connection, with a spherically symmetric metric (cf. [4]), and westudy harmonicity of its sections firstly as smooth maps and then as critical points of the energy functional with variations through smooth sections.We also characterize vertically harmonic sections. Finally, we give some examples of special vector bundles, recovering in some situations some classical harmonicity results.

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来源期刊

Advances in Geometry 数学-数学

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Advances in Geometry is a mathematical journal for the publication of original research articles of excellent quality in the area of geometry. Geometry is a field of long standing-tradition and eminent importance. The study of space and spatial patterns is a major mathematical activity; geometric ideas and geometric language permeate all of mathematics.