Hélices, curvas de Bertrand e superfícies regradas

• Ano de defesa: 2012
• Autor(a) principal: Flôres, Marcia Viaro
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de Santa Maria; BR; Matemática; UFSM; Programa de Pós-Graduação em Matemática
• Palavras-chave em Português: Hélices; Curvas de Bertrand; Superfícies regradas; Helices; Bertrand Curves; Ruled surfaces; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: http://repositorio.ufsm.br/handle/1/9973

This work is designed to study helices and Bertrand curves. A circular helix is characterized by having constant curvature k 6= 0 and constant torsion t . If the ratio t k is constant, the curve is called generalized helix. A curve g : I −→R3 is called a Bertrand curve if there is another curve g : I −→R3 such that the normal lines of g and g at s ∈ I are equal. Generalized helices and Bertrand curves can be viewed as generalizations of the circular helix. In this work, we obtain important characterizations of these curves. Besides, we also study these curves from the view point of the theory of curves on ruled surfaces.