Complete noncompact submanifolds of manifolds with negative curvature

Jing Mao; Ya Gao; Yanling Gao; Zhiqi Xie

doi:10.4134/JKMS.j230283

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Complete noncompact submanifolds of manifolds with negative curvature

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sectional curvature ends submanifolds $L^{p}$ harmonic 1-forms $k$-th Ricci curvature

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초록

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: \begin{itemize} \item several one-end theorems for $M$; \item two Liouville theorems for harmonic maps from $M$ to complete Riemannian manifolds with nonpositive sectional curvature. \end{itemize}

Abstract

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: \begin{itemize} \item several one-end theorems for $M$; \item two Liouville theorems for harmonic maps from $M$ to complete Riemannian manifolds with nonpositive sectional curvature. \end{itemize}

참고문헌 (45)

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