@Article{JMS-56-279,
author = {Bai , Jin-Chuan and Luo , Yong},
title = {Remarks on Gap Theorems for Complete Hypersurfaces with Constant Scalar Curvature},
journal = {Journal of Mathematical Study},
year = {2023},
volume = {56},
number = {3},
pages = {279--290},
abstract = {<p style="text-align: justify;">Assume that $M^n(n\geq3)$ is a complete hypersurface in $\mathbb{R}^{n+1}$ with zero scalar curvature. Assume that $B, H, g$ is the second fundamental form, the mean curvature and the induced metric of $M$, respectively. We prove that $M$ is a hyperplane if $$-P_1(\nabla H,\nabla|H|)\leq-\delta|H||\nabla H|^2$$ for some positive constant $\delta$, where $P_1=nHg-B$ which denotes the first order Newton transformation, and $$\left(\int_M|H|^ndv\right)^\frac{1}{n}&lt;\alpha$$ for some small enough positive constant $\alpha$ which depends only on $n$ and $\delta$. We also derive similar result for complete hypersurfaces in $\mathbb{S}^{n+1}$ with constant scalar curvature $R=n(n-1)$.</p>},
issn = {2617-8702},
doi = {https://doi.org/10.4208/jms.v56n3.23.02},
url = {http://global-sci.org/intro/article_detail/jms/21873.html}
}