Existence and uniqueness theorem for Frenet frame supercurves


In the first part of this paper,using the Banach Grassmann algebra B<sub>L</sub> given by Rogers in her paper [10],a new scalar product and a new definition of the orthogonality are introduced on the (m,n)-dimensional total supereuclidean space {B<sub>L</sub>}<sup>m+n</sup>. Using the GH∈fty functions given by Rogers in [10], the new definitions of the supercurve, of the supersmooth supercurve, of the supersmooth supercurve in general position and of the Frenet frame associated to a supersmooth supercurve in general position are given. In second part of this paper, using the classical results described in [9], the new existence and uniqueness theorem for some supercurves which admit Frenet frame is proved.

DOI Code: 10.1285/i15900932v24n1p143

Keywords: $(m, n)$-dimensional total supereuclidean space ${BL}m+n$; The $(m, n)$-dimensional supereuclidean space ${BL}m+n$; The $GH$ functions; Supersmooth supercurve; Supersmooth supercurve in general position; Frenet frame associated to a supersmooth supercurve; Frenet formulas for the supersmooth supercurve

Classification: 58A50

Full Text: PDF

Creative Commons License
This work is licensed under a Creative Commons Attribuzione - Non commerciale - Non opere derivate 3.0 Italia License.