Acta Mathematica Hungarica

, Volume 94, Issue 4, pp 307–320 | Cite as

Contributions to the Study of Monotone Vector Fields

  • J. X. Da Cruz Neto
  • O. P. Ferreira
  • L. R. Lucambio pérez


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.

monotone vector field Riemannian manifold convex function 


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Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • J. X. Da Cruz Neto
    • 1
  • O. P. Ferreira
    • 1
  • L. R. Lucambio pérez
    • 1
  1. 1.DM/CCN/Universidade Federal Do PiauíTeresina, PiBrazil

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