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Loops and quasigroups: Aspects of current work and prospects for the future

Jonathan D. H. Smith (2000)

Commentationes Mathematicae Universitatis Carolinae

This paper gives a brief survey of certain recently developing aspects of the study of loops and quasigroups, focussing on some of the areas that appear to exhibit the best prospects for subsequent research and for applications both inside and outside mathematics.

Lorentzian isothermic surfaces and Bonnet pairs

M. A. Magid (2004)

Annales Polonici Mathematici

Lorentzian surfaces in Lorentz three-space are studied using an indefinite version of the quaternions. A classification theorem for Bonnet pairs in Lorentz three-space is obtained.

Mean directionally curved lines on surfaces immersed in R4.

Luis Fernando Mello (2003)

Publicacions Matemàtiques

The notion of principal configuration of immersions of surfaces into R3, due to Sotomayor and Gutierrez [16] for lines of curvature and umbilics, is extended to that of mean directional configuration for immersed surfaces in R4. This configuration consists on the families of mean directionally curved lines, along which the second fundamental form points in the direction of the mean curvature vector, and their singularities, called here H-singularities.

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