On the Singularities of Families of Curve Congruences on Lorentzian Surfaces

Autor(es)

Nabarro, Ana Claudia ^[1] ; Saloom, Amani ^[2]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Inst Ciencias Matemat & Comp, Dept Matemat, Campus Sao Carlos, Caixa Postal 668, BR-13560970 Sao Carlos, SP - Brazil

^[2] King Abdulaziz Univ, Dept Math, Fac Sci, POB 80203, Jeddah 21589 - Saudi Arabia

• Tipo de documento: Artigo Científico
• Fonte: JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS; v. 22, n. 3, p. 507-530, JUL 2016.
• Citações Web of Science: 0

Resumo

In Nabarro (2011), we define and study the families of oe{''}-conjugate curve congruences and the families of reflected oe{''}-conjugate curve congruences , i = 1, 2, associated to a self-adjoint operator oe{''} on a smooth and oriented surface M endowed with a Lorentzian metric. These families parametrize parts of the pencils of forms that link the equation of the oe{''}-asymptotic (resp. oe{''}-characteristic) curves and that of the oe{''}-principal curves. There is a crucial difference with the Riemannian case due to the existence of lightlike curves. In this paper, we study the generic local singularities in the members of these families and describe the way they bifurcate within the families. (AU)

• Processo FAPESP: 10/16717-3 - Sobre a geometria de subvariedades no espaço de Minkowski
• Beneficiário: Ana Claudia Nabarro
• Modalidade de apoio: Bolsas no Exterior - Pesquisa