[5] viXra:1902.0444 [pdf] replaced on 2019-02-26 08:55:44
Authors: Madhur Sorout
Comments: 13 Pages.
This paper is mainly focused on the equivalence of closed figures and infinitely extended
lines. Using this principle, some major conclusions can be drawn. The equivalence of closed
figures and infinitely extended lines is mainly based on the idea that closed figures and
infinitely extended lines are equivalent. One of the most significant conclusions drawn from
this equivalency is that if any object moves along a straight infinitely extended line, it will
return back to the point, where it started to move, after some definite time. This principle of
equivalence of closed figures and infinitely extended lines may lead us to understand the
physical reality of infinities.
Category: Geometry
[4] viXra:1902.0401 [pdf] replaced on 2019-04-16 08:32:36
Authors: Eckhard Hitzer
Comments: 16 Pages. published in Adv. of App. Cliff. Algs., 29:46, pp. 1-16, 2019. DOI: 10.1007/s00006-019-0964-1, 1 table.
This work explains how three dimensional quadrics can be defined by the outer products of conformal geometric algebra points in higher dimensions. These multivector expressions code all types of quadrics in arbitrary scale, location and orientation. Furthermore, a newly modified (compared to Breuils et al, 2018, https://doi.org/10.1007/s00006-018-0851-1.) approach now allows not only the use of the standard intersection operations, but also of versor operators (scaling, rotation, translation). The new algebraic form of the theory will be explained in detail.
Category: Geometry
[3] viXra:1902.0370 [pdf] submitted on 2019-02-21 09:48:48
Authors: Antoine Balan
Comments: 1 page, written in english
We define the notion of G-connections over vector fiber bundles with action of a Lie group G.
Category: Geometry
[2] viXra:1902.0283 [pdf] submitted on 2019-02-16 15:24:00
Authors: Antoine Balan
Comments: 1 page, written in english
We construct a symplectic Laplacian which is a differential operator of order 1 depending only on a connection and a symplectic form.
Category: Geometry
[1] viXra:1902.0028 [pdf] submitted on 2019-02-02 12:41:24
Authors: Antoine Balan
Comments: 1 page, written in english
We propose a generalization of the Clifford algebra. We give application to the Dirac operator.
Category: Geometry