Abstract
In this paper, we obtain a rigidity theorem by modifying Cheng–Yau’s technique to linear Weingarten submanifolds in the unit sphere Sn+p(1) with parallel normalized mean curvature vector. As a corollary, we have Theorem 1.3 in Guo and Li (Tohoku Math J 65:331–339, 2013) and Theorem 2 in Li (Math Ann 305:665–672, 1996).
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