Abstract
We generalize Hadamard-Stoker-Currier Theorems for surfaces immersed in a Killing submersion over a strictly Hadamard surface whose fibers are the trajectories of a unit Killing field. We prove that every complete surface whose principal curvatures are greater than a certain function (depending on the ambient manifold) at each point, must be properly embedded, homeomorphic either to the sphere or to the plane and, in the latter case, we study the behavior of the end.
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The author is partially supported by Spanish MEC-FEDER Grant MTM2010-19821 and CNPq-Brazil.
The author is partially supported by Brazilian Fundačcão de Amparo à Pesquisa do Estado do Amazonas — FAPEAM.
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Espinar, J.M., de Oliveira, I.S. Locally convex surfaces immersed in a Killing submersion. Bull Braz Math Soc, New Series 44, 155–171 (2013). https://doi.org/10.1007/s00574-013-0007-9
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DOI: https://doi.org/10.1007/s00574-013-0007-9