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Mean curvature of hypersurfaces in Killing submersions with bounded shadow
Author(s) -
Gimeno Vicent
Publication year - 2020
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201800089
Subject(s) - mathematics , immersion (mathematics) , hypersurface , mean curvature , bounded function , vector field , killing vector field , mathematical analysis , manifold (fluid mechanics) , curvature , norm (philosophy) , pure mathematics , geometry , mechanical engineering , engineering , political science , law
Given a complete hypersurface isometrically immersed in an ambient manifold, in this paper we provide a lower bound for the norm of the mean curvature vector field of the immersion assuming that: 1) The ambient manifold admits a Killing submersion with unit‐length Killing vector field. 2) The projection of the image of the immersion is bounded in the base manifold. 3) The hypersurface is stochastically complete, or the immersion is proper.