Hélices, curvas de Bertrand e superfícies regradas

• Autor(a) principal: Flôres, Marcia Viaro
• Data de Publicação: 2012
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Manancial - Repositório Digital da UFSM
• dARK ID: ark:/26339/0013000017538
• Texto Completo: http://repositorio.ufsm.br/handle/1/9973
• topic: Hélices; Curvas de Bertrand; Superfícies regradas; Helices; Bertrand Curves; Ruled surfaces; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA

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.