Journal of the
Korean Mathematical Society

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

Ahead of Print Articles


J. Korean Math. Soc.

Online first article October 23, 2023

Copyright © The Korean Mathematical Society.

Complete noncompact submanifolds of manifolds with negative curvature

Ya Gao, Yanling Gao, Jing Mao, and Zhiqi Xie

Hubei University, Yulin University


In this paper, for a $m$-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 $|\textbf{H}_{f}|$ and the weighted real-valued function $f$, we can obtain:
several one-end theorems for $M$;
two Liouville theorems for harmonic maps from $M$ to complete Riemannian manifolds with nonpositive sectional curvature.

Keywords: $L^{p}$ harmonic 1-forms; Submanifolds; Ends; Sectional curvature; $k$-th Ricci curvature.

MSC numbers: 53C20, 53C42.

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