具有 $h$-近 Ricci 孤立子结构的双重卷积流形

数学物理学报 ›› 2026, Vol. 46 ›› Issue (5): 1685-1690.

具有 $h$-近 Ricci 孤立子结构的双重卷积流形

王霄雪(), 刘建成^*()

西北师范大学数学与统计学院兰州 730070

收稿日期:2025-03-28 修回日期:2025-07-09 出版日期:2026-10-26 发布日期:2026-09-07
通讯作者: 刘建成 E-mail:2837759265@qq.com;liujc@nwnu.edu.cn
作者简介:王霄雪,E-mail:2837759265@qq.com
基金资助:
国家自然科学基金(12161078);甘肃省基础研究创新群体项目(24JRRA778)

Doubly Warped Product Manifolds with the Structure of $h$-Almost Ricci Solitons

Xiaoxue Wang(), Jiancheng Liu^*()

College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070

Received:2025-03-28 Revised:2025-07-09 Online:2026-10-26 Published:2026-09-07
Contact: Jiancheng Liu E-mail:2837759265@qq.com;liujc@nwnu.edu.cn
Supported by:
NSFC(12161078);Innovative Fundamental Research Group Project of Gansu Province(24JRRA778)

摘要/Abstract

摘要：

该文研究具有 $h$-近 Ricci 孤立子结构的双重卷积流形,给出了双重卷积流形是 $h$-近 Ricci 孤立子的充要条件, 证明了在一定条件下,具有 $h$-近 Ricci 孤立子结构的双重卷积流形及其基流形和纤维流形均为 Einstein 流形.

关键词: $h$-近 Ricci 孤立子, 双重卷积流形, Einstein 流形

Abstract:

This paper investigates doubly warped product manifolds endowed with an $h$-almost Ricci soliton structure. We establish the necessary and sufficient conditions for a doubly warped product manifold to be an $h$-almost Ricci soliton. Furthermore, we prove that under certain conditions, doubly warped product manifolds with an $h$-almost Ricci soliton structure, along with their base and fiber manifolds, are all Einstein manifolds.

Key words: $h$-almost Ricci soliton, doubly warped product manifold, Einstein manifold

中图分类号:

O186.12

王霄雪, 刘建成. 具有 $h$-近 Ricci 孤立子结构的双重卷积流形[J]. 数学物理学报, 2026, 46(5): 1685-1690.

Xiaoxue Wang, Jiancheng Liu. Doubly Warped Product Manifolds with the Structure of $h$-Almost Ricci Solitons[J]. Acta mathematica scientia,Series A, 2026, 46(5): 1685-1690.

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