A maximum principle at infinity with applications to geometric vector fields

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:474

Article

Alias, L. J.¹  Caminha, A.²  do Nascimento, F. Y.³ 

[1] Univ Murcia, Dept Matemat, E-30100 Murcia, Spain

[2] Univ Fed Ceara, Dept Matemat, Campus Pici, BR-60455760 Fortaleza, Ce, Brazil

[3] Univ Fed Ceara, BR 226,Km 4, Crateus, Ceara, Brazil

关键词: Killing fields;    Riemannian groups;    Lorentzian groups;    Totally geodesic hypersurfaces;    Maximum principle;   

DOI  :  10.1016/j.jmaa.2019.01.042

来源: Elsevier

【 摘 要 】

We derive a new form of maximum principle, applicable to a vector field with nonnegative divergence in a connected, oriented, complete noncompact Riemannian manifold. We then use it to obtain some applications to Killing vector fields. More precisely, we first show that, under a reasonable condition at infinity, an orientable, connected, complete noncompact hypersurface of a Riemannian manifold, transversal to a Killing vector field of constant norm and with nonnegative second fundamental form, is totally geodesic. We also deal with the case of a hypersurface of constant mean curvature - instead of nonnegative second fundamental form, and show that it has to be totally geodesic too. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free