Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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COMPLETE NONCOMPACT SUBMANIFOLDS OF MANIFOLDS WITH NEGATIVE CURVATURE

  • Ya Gao (Faculty of Mathematics and Statistics Key Laboratory of Applied Mathematics of Hubei Province Hubei University) ;
  • Yanling Gao (Faculty of Mathematics and Statistics Key Laboratory of Applied Mathematics of Hubei Province Hubei University) ;
  • Jing Mao (Faculty of Mathematics and Statistics Key Laboratory of Applied Mathematics of Hubei Province Hubei University) ;
  • Zhiqi Xie (School of Mathematics and Statistics Yulin University)
  • Received : 2023.05.31
  • Accepted : 2023.08.16
  • Published : 2024.01.01
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Abstract

In this paper, for an m-dimensional (m ≥ 5) complete non-compact submanifold M immersed in an n-dimensional (n ≥ 6) 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 |Hf| 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

Acknowledgement

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).

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