Total torsion of curves in three-dimensional manifolds

Autor(es)

Pansonato, Claudia C. ^[1] ; Costa, Sueli I. R. ^[2]

Afiliação do(s) autor(es)

^[1] Univ Fed Santa Maria, Dept Math, CCNE, BR-97105900 Santa Maria, RS - Brazil

^[2] Univ Estadual Campinas, UNICAMP, Inst Math, BR-13083970 Campinas, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Geometriae Dedicata; v. 136, n. 1, p. 111-121, OCT 2008.
• Citações Web of Science: 1

Resumo

A classical result in differential geometry assures that the total torsion of a closed spherical curve in the three-dimensional space vanishes. Besides, if a surface is such that the total torsion vanishes for all closed curves, it is part of a sphere or a plane. Here we extend these results to closed curves in three dimensional Riemannian manifolds with constant curvature. We also extend an interesting companion for the total torsion theorem, which was proved for surfaces in R(3) by L. A. Santalo, and some results involving the total torsion of lines of curvature. (AU)

• Processo FAPESP: 02/07473-7 - Códigos geometricamente uniformes em espaços homogêneos
• Beneficiário: Sueli Irene Rodrigues Costa
• Modalidade de apoio: Auxílio à Pesquisa - Temático