Tzitzeica curves and surfaces represent early examples of affineinvariant geometrical objects. At the time Gheorghe Tzitzeica was studying these objects, affine differential geometry (ADG) was in its infancy. ADG was motivated by Felix Kleinʼs influential Erlangen program, where a geometry was defined by its set of invariants under a group of symmetries. We find that the issue lends itself well to a relatively elementary discussion suitable for upper-division undergraduates and nonspecialists, while still providing the basic thrust of this elegant subject. Moreover, the topic is an excellent one to illustrate the utility of Mathematicaʼs symbolic manipulation and graphics capabilities. For this reason, the article nicely complements the existing literature on the uses of software in differential geometry (such as [1]), and it provides material that would be useful for inclusion in a differential geometry course either as an application or a project.

In this article we introduce three centro-affine invariant functions in Minkowski spaces. Tzitzeica curves and Tzitzeica surfaces may be defined in this new context. Our main results allow us to understand the connections between Tzitzeica curves and surfaces in Minkowski spaces and the original Tzitzeica curves and surfaces from the Euclidian space

at Fullerton. His main fields of research include affine differential geometry, asymptotic analysis, twistor theory, geometric algebra and their applications in physics. Alexandru Bobe received his Ph.D. in 2007. Presently, he is an assistant professor at the Ovidius University in Constanţa, Romania. His main fields of research include affine differential geometry, Riemannian geometry, computational algebra and geometry.

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