LINEAR WEINGARTEN HYPERSURFACES IN RIEMANNIAN SPACE FORMS Chao, Xiaoli; Wang, Peijun;
Abstract
In this note, we generalize the weak maximum principle in [4] to the case of complete linear Weingarten hypersurface in Riemannian space form (c = 1, 0,-1), and apply it to estimate the norm of the total umbilicity tensor. Furthermore, we will study the linear Weingarten hypersurface in with the aid of this weak maximum principle and extend the rigidity results in Li, Suh, Wei [13] and Shu [15] to the case of complete hypersurface.
Keywords
linear Weingarten hypersurface;maximum principle;space form;Clifford torus;circular cylinder;hyperbolic cylinder;
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