J. Korean Math. Soc. 2024; 61(1): 183-205
Online first article October 23, 2023 Printed January 1, 2024
https://doi.org/10.4134/JKMS.j230283
Copyright © The Korean Mathematical Society.
Ya Gao , Yanling Gao, Jing Mao , Zhiqi Xie
Hubei University; Hubei University; Hubei University; Yulin University
In this paper, for an $m$-dimensional ($m\geq5$) complete noncompact submanifold $M$ immersed in an $n$-dimensional ($n\geq6$) simply connected Riemannian manifold $N$ with negative sectional curvature, under suitable constraints on the squared norm of the second fundamental form of $M$, the norm of its weighted mean curvature vector $|\textbf{\emph{H}}_{f}|$ and the weighted real-valued function $f$, we can obtain:
Keywords: $L^{p}$ harmonic 1-forms, submanifolds, ends, sectional curvature, $k$-th Ricci curvature
MSC numbers: 53C20, 53C42
Supported by: This work is partially supported by the NSF of China (Grant Nos. 11801496, 11926352 and 12261095), the Fok Ying-Tung Education Foundation (China) and Hubei Key Laboratory of Applied Mathematics (Hubei University).
2004; 41(5): 795-808
2011; 48(1): 23-31
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