Geometry

1902 Submissions

[5] viXra:1902.0444 [pdf] replaced on 2019-02-26 08:55:44

On the Equivalence of Closed Figures and Infinitely Extended Lines and the Conclusions Drawn from it

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

Three-Dimensional Quadrics in Conformal Geometric Algebras and Their Versor Transformations

Authors: Eckhard Hitzer
Comments: Submitted to Topical Collection of Adv. in Appl. Clifford Algebras, for Proceedings of AGACSE 2018, 23 Feb. 2019, 15 pages. 4 errors corrected: 25 Feb. 2019. Proposition 4.1 corrected: 02 Mar. 2019. Further revision: 16 Apr. 2019.

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

The G-connections

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

The Symplectic Laplacian

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

A Generalized Clifford Algebra

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