New characterizations of hyperbolic cylinders in semi-Riemannian space forms

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• 作者：Henrique F. de Lima ; ^{henrique@mat.ufcg.edu.br" class="auth_mail" title="E-mail the corresponding author} ; Fá ; bio R. dos Santos ^{fabio@mat.ufcg.edu.br" class="auth_mail" title="E-mail the corresponding author} ; Marco Antonio L. Velá ; squez ^{marco.velasquez@pq.cnpq.br" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Semi-Riemannian space forms ; Parallel normalized mean curvature vector ; Complete linear Weingarten submanifold ; Isoparametric submanifolds ; Hyperbolic cylinders
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2016
• 出版时间：1 February 2016
• 年：2016
• 卷：434
• 期：1
• 页码：765-779
• 全文大小：394 K

文摘

Through the study of the so-called linear Weingarten spacelike submanifolds immersed with parallel normalized mean curvature vector in a semi-Riemannian space form class="mathmlsrc">title="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X15008628&_mathId=si1.gif&_user=111111111&_pii=S0022247X15008628&_rdoc=1&_issn=0022247X&md5=58128f4018706dee05da5a23d714313a">class="imgLazyJSB inlineImage" height="22" width="56" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0022247X15008628-si1.gif">class="mathContainer hidden">class="mathCode">${\mathbb{Q}}_p^{n+p}(c)$ of index p   and constant sectional curvature class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X15008628&_mathId=si2.gif&_user=111111111&_pii=S0022247X15008628&_rdoc=1&_issn=0022247X&md5=429e99eb2dc019bf080e2ab98912cb85" title="Click to view the MathML source">c∈{−1,0,1}class="mathContainer hidden">class="mathCode">$c\in \{-1,0,1\}$, our aim in this paper is establish new characterizations for the hyperbolic cylinders of class="mathmlsrc">title="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X15008628&_mathId=si1.gif&_user=111111111&_pii=S0022247X15008628&_rdoc=1&_issn=0022247X&md5=58128f4018706dee05da5a23d714313a">class="imgLazyJSB inlineImage" height="22" width="56" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0022247X15008628-si1.gif">class="mathContainer hidden">class="mathCode">${\mathbb{Q}}_p^{n+p}(c)$. Our approach is based on the use of a Simons type formula related to an appropriated Cheng–Yau modified operator jointly with the application of suitable generalized maximum principles.