关于常曲率空间中子流形$p$-调和$\ell$-形式的一个消灭定理

数学物理学报 ›› 2024, Vol. 44 ›› Issue (1): 26-36.

关于常曲率空间中子流形$p$-调和$\ell$-形式的一个消灭定理

张友花()

福建师范大学数学与统计学院福州 350000

收稿日期:2022-10-08 修回日期:2023-09-28 出版日期:2024-02-26 发布日期:2024-01-10
作者简介:张友花, E-mail：505289305@qq.com
基金资助:
国家自然科学基金(2021J01165)

A Vanishing Theorem for$p$-harmonic$\ell$-forms in Space with Constant Curvature

Zhang Youhua()

Fujian Normal University, Fuzhou 350000

Received:2022-10-08 Revised:2023-09-28 Online:2024-02-26 Published:2024-01-10
Supported by:
NSFC(2021J01165)

摘要/Abstract

摘要：

令$M^{n}(n \geq 3)$是常曲率空间$N^{n+m}(c)$中的、具有平坦法丛的完备非紧致的浸入子流形. 假设$M^{n}(n \geq 3)$满足四个不同的具体几何条件之一时, 该文利用 Bochner-Weitzenböck 公式和 Sobolev 不等式, 通过 Duzaar-Fuchs 截断函数方法, 证明了$M^{n}$上不存在非平凡的$L^{\beta}~p$-调和$\ell$-形式, 其中$\beta\geq p\geq 2$.

关键词: 子流形, $p$-调和形式, 消灭性定理

Abstract:

Let$M^{n}(n \geq 3)$be a complete non-compact submanifold immersed in a space with constant curvature$N^{n+m}(c)$with flat normal bundle. By using Bochner-Weitzenböck formula, Sobolev inequality, Moser iteration and Fatou lemma, we prove that every$L^{\beta}~p$-harmonic forms on$M$is trivial if$M^{n}$satisfies some geometic conditions, where$\beta\geq p\geq 2$.

Key words: Submanifold, $p$-harmonic form, Vanishing theorem

中图分类号:

O186.12

张友花. 关于常曲率空间中子流形$p$-调和$\ell$-形式的一个消灭定理[J]. 数学物理学报, 2024, 44(1): 26-36.

Zhang Youhua. A Vanishing Theorem for$p$-harmonic$\ell$-forms in Space with Constant Curvature[J]. Acta mathematica scientia,Series A, 2024, 44(1): 26-36.

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