Monotone point-to-set vector field
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Data
2000
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Resumo
We introduce the concept of monotone point-to-set field in Riemannian man-
ifold and give a characterization, that make clear in this definition the occult
geometric meaning. We will show that the sub-differential operator of a Rieman-
nian convex function is a monotone point-to-set field. The concept of directional
derivative, which appears already in other publications, plays an important role
in the proof of the result above. We study some of its properties, in particular,
we obtain the chain rule, which is fundamental in our work. Some topological
consequences of the existence of strictly monotone point-to-set fields are pre-
sented.
Descrição
Palavras-chave
Parallel transport, Directional derivative, Riemannian convexity, Monotone point-to-set vector field
Citação
CRUZ NETO, J. X. ; FERREIRA, O. P. ; LUCAMBIO PÉREZ, L. R. Monotone point-to-set vector field. Balkan Journal of Geometry and its Applications, Bucharest, v. 5, n.1, p. 69-79, 2000.