具有多重卷积结构的梯度 h ˜ -近Ricci孤立子
Gradient h ˜ -Almost Ricci Solitons with Multiply Warped Product Structure
DOI: 10.12677/pm.2026.169196, PDF,    科研立项经费支持
作者: 赵晓慧, 刘建成*：西北师范大学数学与统计学院，甘肃 兰州
关键词: 多重卷积流形；梯度-近Ricci孤立子；不存在性；Multiply Warped Product Manifolds； Gradient -Almost Ricci Soliton； Nonexistence
摘要: 该文得到了具有多重卷积结构的黎曼流形是梯度 h ˜ -近Ricci孤立子的充要条件。作为应用，在关于卷积函数或基流形和纤维流形上梯度向量场的一些自然假设下，运用强极值原理，证明了具有多重卷积结构的梯度 h ˜ -近Ricci孤立子的不存在性结果，即这样的孤立子只能是黎曼直积流形。
Abstract: In this paper, we derive necessary and sufficient conditions for a multiply warped product manifold to be a gradient h ˜ -almost Ricci soliton. As applications, under some natural assumptions on the warping functions or the gradient vector fields on the base and fiber manifolds, we obtain the nonexistence results of gradient h ˜ -almost Ricci solitons with multiply warped product structure by applying the strong maximum principle, i.e., such solitons are Riemannian product manifolds.
文章引用：赵晓慧, 刘建成. 具有多重卷积结构的梯度 h ˜ -近Ricci孤立子[J]. 理论数学, 2026, 16(9): 35-46. https://doi.org/10.12677/pm.2026.169196

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