Boundedness of geometric invariants near a singularity which is a suspension of a singular curve

Authors

  • Luciana F. Martins Universidade Estadual Paulista (UNESP), Instituto de Biociências Letras e Ciências Exatas, R. Cristóvão Colombo, 2265, Jd Nazareth, 15054-000, São Josê do Rio Preto, São Paulo, Brazil
  • Kentaro Saji Department of Mathematics, Graduate School of Science, Kobe University, Rokkodai 1-1, Nada, Kobe, 657-8501, Japan
  • Samuel P. dos Santos Universidade Estadual Paulista (UNESP), Instituto de Biociências Letras e Ciências Exatas, R. Cristóvão Colombo, 2265, Jd Nazareth, 15054-000, São Josê do Rio Preto, São Paulo, Brazil
  • Keisuke Teramoto Graduate School of Sciences and Technology for Innovation, Yamaguchi University, Yamaguchi, 753-8512, Japan

DOI:

https://doi.org/10.33044/revuma.3492

Abstract

Near a singular point of a surface or a curve, geometric invariants diverge in general, and the orders of this divergence, in particular the boundedness about these invariants, represent the geometry of the surface and the curve. In this paper, we study the boundedness and orders of several geometric invariants near a singular point of a surface which is a suspension of a singular curve in the plane, and those of the curves passing through the singular point. We evaluate the orders of the Gaussian and mean curvatures, as well as those of the geodesic and normal curvatures, and the geodesic torsion for the curve.

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Author Biography

Luciana F. Martins, Universidade Estadual Paulista (UNESP), Instituto de Biociências Letras e Ciências Exatas, R. Cristóvão Colombo, 2265, Jd Nazareth, 15054-000, São Josê do Rio Preto, São Paulo, Brazil

Departamento de Matematica, Ibilce,
Universidade Estadual Paulista

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Published

2024-09-23

Issue

Vol. 67 No. 2 (2024)

Section

Article

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Copyright (c) 2024 Luciana F. Martins, Kentaro Saji, Samuel P. dos Santos, Keisuke Teramoto

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