Spinor formulation of the differential geometry of curves

Published

2004-01-01

Spinor formulation of the differential geometry of curves

Keywords:

Frenet equations, Spinors, 2000 Mathematics Subject Classification, Primary: 55A04. Secondary: 15A66. (en)

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Authors

Universidad Autónoma de Puebla, México
Universidad Autónoma de Puebla, México

Abstract (en)

Abstract. It is shown that the Frenet equations for curves in R³ can be reduced to a single equation for a vector with two complex components and some examples of the usefulness of this representation are given.

References

E. CARTAN, The theory of spinors, Hermann, Paris, 1966. (Dover, New York, reprinted 1981.)

W. T. PAYNE, Elementary spinor theory, Am. J. of Phys. 20 (1952) 253.

G. F. Torres del Castillo, 3-D Spinors, Spin-Weighted Functions and their Applications, Birkhâuser, Boston, 2003.

D. H. Sattinger &: O. L. Weaver, Lie Groups and Algebras with Applications to Physics, Geometry and Mechanics, Springer-Verlag, New York, 1986.

H. Goldstein, Classical mechanics, 2nd ed., Addison-Wesley, Reading, Mass., 1980.

B. O ’Neill, Elementary differential geometry, 2nd ed., Academic Press, San Diego, 1997.

J. Oprea, Differential geometry and its applications, Prentice-Hall, Upper Saddle River, N. J., 1997.

How to Cite

APA

Gerardo Francisco and Guadalupe. (2004). Spinor formulation of the differential geometry of curves. Revista Colombiana de Matemáticas, 38(1), 27–34. https://revistas.unal.edu.co/index.php/recolma/article/view/94309

ACM

[1]

Gerardo Francisco and Guadalupe 2004. Spinor formulation of the differential geometry of curves. Revista Colombiana de Matemáticas. 38, 1 (Jan. 2004), 27–34.

ACS

(1)

Gerardo Francisco; Guadalupe. Spinor formulation of the differential geometry of curves. rev.colomb.mat 2004, 38, 27-34.

ABNT

GERARDO FRANCISCO; GUADALUPE. Spinor formulation of the differential geometry of curves. Revista Colombiana de Matemáticas, [S. l.], v. 38, n. 1, p. 27–34, 2004. Disponível em: https://revistas.unal.edu.co/index.php/recolma/article/view/94309. Acesso em: 10 mar. 2025.

Chicago

Gerardo Francisco, and Guadalupe. 2004. “Spinor formulation of the differential geometry of curves”. Revista Colombiana De Matemáticas 38 (1):27-34. https://revistas.unal.edu.co/index.php/recolma/article/view/94309.

Harvard

Gerardo Francisco and Guadalupe (2004) “Spinor formulation of the differential geometry of curves”, Revista Colombiana de Matemáticas, 38(1), pp. 27–34. Available at: https://revistas.unal.edu.co/index.php/recolma/article/view/94309 (Accessed: 10 March 2025).

IEEE

[1]

Gerardo Francisco and Guadalupe, “Spinor formulation of the differential geometry of curves”, rev.colomb.mat, vol. 38, no. 1, pp. 27–34, Jan. 2004.

MLA

Gerardo Francisco, and Guadalupe. “Spinor formulation of the differential geometry of curves”. Revista Colombiana de Matemáticas, vol. 38, no. 1, Jan. 2004, pp. 27-34, https://revistas.unal.edu.co/index.php/recolma/article/view/94309.

Turabian

Gerardo Francisco, and Guadalupe. “Spinor formulation of the differential geometry of curves”. Revista Colombiana de Matemáticas 38, no. 1 (January 1, 2004): 27–34. Accessed March 10, 2025. https://revistas.unal.edu.co/index.php/recolma/article/view/94309.

Vancouver

1.

Gerardo Francisco, Guadalupe. Spinor formulation of the differential geometry of curves. rev.colomb.mat [Internet]. 2004 Jan. 1 [cited 2025 Mar. 10];38(1):27-34. Available from: https://revistas.unal.edu.co/index.php/recolma/article/view/94309