Geometry of 2x2 matrix curves

Authors

  • Victor León Instituto Latino-Americano de Ciencias da Vida e da Natureza-ILACVN, Universidade Federal da Integracao Latino-Americana-UNILA, Foz do Iguacu-Parana, Brasil.
  • Newton Solórzano Instituto Latino-Americano de Ciencias da Vida e da Natureza-ILACVN, Universidade Federal da Integracao Latino-Americana-UNILA, Foz do Iguacu-Parana, Brasil.
  • Alexis Rodríguez Instituto de Investigación en Matemáticas, Departamento de Matemáticas, Universidad Nacional de Trujillo, Trujillo, Perú.
  • Karen Gaviria Instituto Latino-Americano de Tecnologia, Infraestrutura e Território - ILATIT, Universidade Federal da Integração Latino- Americana - UNILA, Foz do Iguaçu - Paraná, Brasil.

DOI:

https://doi.org/10.17268/sel.mat.2022.02.04

Keywords:

Matrix curves, Gram-Schmidt orthogonalization process, Frenet-Serret formulas, fundamental theorem of curves

Abstract

In this work, we study the geometry of 2x2 order matrix curves with real coefficients. We use the Gram-Schmidt orthogonalization process to generate a convenient moving benchmark. Thus, we obtain the Frenet-Serret formulas. We present a version of the fundamental theorem of 2x2 matrix curves.

References

Benazic R. Tópicos de ecuaciones diferenciales ordinarias. Lima: UNI; 2007.

Coddington EA. An introduction to ordinary differential equations. New York: Dover Publications; 1989.

De Almeida Junior RV. Estimadores de curvaturas para curvas no R^4. Rio de Janeiro: Pontifícia Universidade Católica do Rio de Janeiro; 2011. Dissertação de mestrado.

Friedberg SH, Insel AJ, Spence LE. Linear algebra. 4th ed. New Delhi: Pearson New International Edition; 2013.

Lang S. Linear algebra. Undergraduate Texts in Mathematics. 3th ed. New York: Springer; 1987.

Tenenblat K, Introdução à geometria diferencial. 2.ed. São Paulo: Blucher; 2008.

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Published

2022-12-30

How to Cite

León, V., Solórzano, N., Rodríguez, A. ., & Gaviria, K. (2022). Geometry of 2x2 matrix curves. Selecciones Matemáticas, 9(02), 258 - 274. https://doi.org/10.17268/sel.mat.2022.02.04

Issue

Vol. 9 No. 02 (2022): August - December

Section

Articles

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