The energy density of biharmonic quadratic maps between spheres

IF 0.6 4区数学 Q3 MATHEMATICS Differential Geometry and its Applications Pub Date : 2023-12-21 DOI:10.1016/j.difgeo.2023.102096

Rareş Ambrosie, Cezar Oniciuc

引用次数: 0

Abstract

In this paper, we first prove that a quadratic form from $S^{m}$ to $S^{n}$ is non-harmonic biharmonic if and only if it has constant energy density $(m + 1) / 2$ . Then, we give a positive answer to an open problem raised in [1] concerning the structure of non-harmonic biharmonic quadratic forms. As a direct application, using classification results for harmonic quadratic forms, we infer classification results for non-harmonic biharmonic quadratic forms.

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球间双谐波二次映射的能量密度

在本文中，我们首先证明，当且仅当从 Sm 到 Sn 的二次型具有恒定的能量密度 (m+1)/2 时，它是非谐波双谐波的。然后，我们给出了[1]中提出的关于非谐波双谐二次型结构的开放问题的正面答案。作为直接应用，我们利用谐二次型的分类结果来推断非谐双谐二次型的分类结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Differential Geometry and its Applications 数学-数学

CiteScore

1.00

自引率

20.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Differential Geometry and its Applications publishes original research papers and survey papers in differential geometry and in all interdisciplinary areas in mathematics which use differential geometric methods and investigate geometrical structures. The following main areas are covered: differential equations on manifolds, global analysis, Lie groups, local and global differential geometry, the calculus of variations on manifolds, topology of manifolds, and mathematical physics.

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