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Anticipation at the Juncture of Geometry and Calculus

p. 194-209

Abstract

The structure "Finslerian teleparallelism" might have been anticipated through a deeper implementation of the ideas that led to great progress in differential geometry in the 20th century. That structure's significance is manifested through the Kähler calculus of differential forms. Based on Clifford algebra, this calculus supersedes Élie Canan's. It revolves around Kähler's equation, a generalization of Dirac's. The juncture of geometry and the calculus is to be understood in the sense that, through the aforementioned implementation, one can create a Kaluza-Klein type structure where the torsion part of the structural equations is given by a fully geometric Kähler equation. Its input is the differential form whose exterior covariant derivative is precisely the torsion in its role as output differential form, thus yielding a closed geometric system of structural equations.

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References

Bibliographical reference

José G. Vargas and Douglas G. Torr, « Anticipation at the Juncture of Geometry and Calculus », CASYS, 19 | 2006, 194-209.

Electronic reference

José G. Vargas and Douglas G. Torr, « Anticipation at the Juncture of Geometry and Calculus », CASYS [Online], 19 | 2006, Online since 23 August 2024, connection on 27 December 2024. URL : http://popups.uliege.be/3041-539x/index.php?id=2484

Authors

José G. Vargas

PST Associates, 48 Hamptonwood Way, Columbia, SC 29209

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Douglas G. Torr

PST Associates, 207 Ridgeview RD., Southern Pines, NC 28388

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