Gheorghe Ţiţeica and the origins of affine differential geometry

Agnew, Alfonso F.; Bobe, Alexandru; Boskoff, Wladimir G.; Suceavă, Bogdan D.

doi:10.1016/j.hm.2008.09.001

Cited by 12 publications

(3 citation statements)

References 16 publications

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“…The affine differential geometry of surfaces is the study of properties of surfaces in three-dimensional space that are invariant under the group of unimodular affine transformations ASL(R 3 ). A survey about the origins of this subject of research can be fond in [1]. Affine differential geometry has been studied by many authors and it is a subject of current research, see for example [7,[15][16][17]26,27,30,33].…”

Section: Affine Differential Geometrymentioning

confidence: 99%

Blaschke's asymptotic lines of surfaces in R3

Barajas-Sichacá,

Garcia,

Vargas

2020

Preprint

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In this paper we consider the Blaschke's asymptotic lines (also called affine asymptotic lines) of regular surfaces in 3-space. We study the binary differential equations defining Blaschke's asymptotic lines in the elliptic and hyperbolic regions of the surface near affine cusp points and to flat affine umbilic points. We also describe the affine asymptotic lines near the Euclidean parabolic set including the Euclidean flat umbilic points.

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Section: Affine Differential Geometrymentioning

confidence: 99%

Blaschke's asymptotic lines of surfaces in R3

Barajas-Sichacá,

Garcia,

Vargas

2020

Preprint

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“…➢ MATLAB LiveScript. In interactive mode, the programmer uses entering commands directly in the command window, [1]. Nevertheless however, when MATLAB software are larger, then there are collections of scripts stored in a common folder.…”

Section: Introductionmentioning

confidence: 99%

A brief introduction to the Matlab program

Tomozei¹,

Axinte²,

Paraschiv³

2023

Technium

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The paper aims just a brief introduction to the MATLAB software. In this article, we study three cases: right triangle, pendulum and simply supported beam. In the first case, we make a right triangle that has the following dimensions: 3m, 4m and 5m. Moreover, in the second case, we calculate the angle αt from a simple pendulum. In the last case, is determined shear force and bending moment only when the uniform distributed load act on the simply supported beam (SSB).

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“…Gheorghe Tzitzeica provided one of the first major contributions to affine differential geometry in the early twentieth century when he published his results on "S-surfaces", later to be known as Tzitzeica surfaces [9,10]. Indeed, these works may be considered to be the starting point of the affine differential geometry as it can be seen in [4] and [6] (for further information on the pioneering work of Ţ iţeica, see [1]).…”

Section: Introductionmentioning

confidence: 99%