Geometria extrínseca de campos de vetores em R3
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2016-05-13
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Universidade Federal de Goiás
Resumo
In this work we first consider regular vector fields : R3 ! R3 and its orthogonal
distribution of planes. We present a characterization of the normal curvature
associated to and the system of implicit differential equations
2(D (dr); dr; ) + h rot( ); i hdr; dri = 0; hdr; i = 0;
which define two one-dimensional singular and orthogonal foliations, which we call by
principal foliations and whose leaves are the principal lines of the distribution .
Next we describe the configurations of the principal foliations in a neighborhood
of the generic singular points that constitutes a regular curve in R3, which are
denoted by Darbouxian umbilic partially points and semi-Darbouxian. We proceed
by studying the stability of the closed principal lines and we also present a Kupka-
Smale genericity result. To conclude, we study the structure of the singularities of
the principal foliations in a neighborhood of a singular hyperbolic point of the vector
field .
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Citação
GOMES, Alacy José. Geometria extrínseca de campos de vetores em R3. 2016. 128 f. Tese (Doutorado em Matemática) - Universidade Federal de Goiás, Goiânia, 2016.