Abstract
We introduce the concept of a strongly monotone vector field on a Riemannian manifold and give an example. We also demonstrate relationships between different kinds of monotonicity of vector fields and different kinds of definiteness of its differential operator. Some topological and metric consequences of the strict and strongly monotone vector fields" existence are shown.
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Da Cruz Neto, J.X., Ferreira, O.P. & Lucambio pérez, L.R. Contributions to the Study of Monotone Vector Fields. Acta Mathematica Hungarica 94, 307–320 (2002). https://doi.org/10.1023/A:1015643612729
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DOI: https://doi.org/10.1023/A:1015643612729