# Geometry

## 1808 Submissions

[3] **viXra:1808.0595 [pdf]**
*submitted on 2018-08-25 08:47:43*

### Definition of the Term "DIRECTION" Определение термина «НАПРАВЛЕНИЕ»

**Authors:** Somsikov A.I.

**Comments:** 2 Pages.

One of initial or primary concepts which is considered to the "protozoa" (who aren't expressed through other concepts) is considered. The structure of this concept is revealed. Algebraic and geometrical consequences are found.
Рассмотрено одно из исходных или первичных понятий, считающееся «простейшим» (не выражаемым через другие понятия). Выявлена структура этого понятия. Найдены алгебраические и геометрические следствия.

**Category:** Geometry

[2] **viXra:1808.0208 [pdf]**
*submitted on 2018-08-15 11:10:29*

### (Ip-GP Version 1.0 15 Pages 14.08.2018) on the Intrinsic Paradox of the Geometric Point Definition (Solved Using the Included Middle Logic) as the Main Cause of Euclid’s Postulate “inaccuracy”, Allowing the Existence not Only of Non-Euclidean Geomet

**Authors:** Andrei Lucian Dragoi

**Comments:** 15 Pages.

This paper brings to attention the intrinsic paradox of the geometric point (GP) definition, a paradox solved in this paper by using Stéphane Lupasco’s Included Middle Logic (IML) (which was stated by Basarab Nicolescu as one of the three pillars of transdisciplinarity [TD]) and its extended form: based on IML, a new “t-metamathematics” (tMM) (including a t-metageometry[tMG]) is proposed, which may explain the main cause of Euclid’s parallel postulate (EPP) “inaccuracy”, allowing the existence not only of non-Euclidean geometries (nEGs), but also the existence of new EPP variants. tMM has far-reaching implications, including the help in redefining the basics of Einstein’s General relativity theory (GRT), quantum field theory (QFT), superstring theories (SSTs) and M-theory (MT).
KEYWORDS (including a list of main abbreviations): geometric point (GP); Stéphane Lupasco’s Included Middle Logic (IML); Basarab Nicolescu, transdisciplinarity (TD); “t-metamathematics” (tMM); t-metageometry (tMG); Euclid’s parallel postulate (EPP); non-Euclidean geometries; new EPP variants; Einstein’s General relativity theory (GRT); quantum field theory (QFT); superstring theories (SSTs); M-theory (MT);

**Category:** Geometry

[1] **viXra:1808.0206 [pdf]**
*replaced on 2018-08-18 16:33:06*

### The Balan-Killing Manifolds

**Authors:** Antoine Balan

**Comments:** 2 pages, written in english

We define here the notion of Balan-Killing manifolds which are spin manifolds whose metrics verify a certain differential equation. We take our inspiration from the notion of Killing spinors.

**Category:** Geometry