[8] **viXra:1904.0494 [pdf]**
*submitted on 2019-04-25 11:47:18*

**Authors:** Antoine Balan

**Comments:** 1 page, written in french

We define a flow for hermitian manifolds. We call it the Hermite-Ricci flow.

**Category:** Geometry

[7] **viXra:1904.0418 [pdf]**
*submitted on 2019-04-21 08:23:26*

**Authors:** Timothy W. Jones

**Comments:** 7 Pages.

Expanding the root form of a polynomial for large numbers of roots can be complicated. Such polynomials can be used to prove the irrationality of powers of pi, so a technique for arriving at expanded forms is needed. We show here how roots of polynomials can generate regular polygons whose vertices considered as roots form known expanded polynomials. The product of these polynomials can be simple enough to yield the desired expanded form.

**Category:** Geometry

[6] **viXra:1904.0398 [pdf]**
*submitted on 2019-04-20 11:06:10*

**Authors:** Yogesh H. Kulkarni, Anil D. Sahasrabudhe, Muknd S. Kale

**Comments:** 4 Pages.

Computer-aided Design (CAD) models of thin-walled parts such as sheet metal or plastics are often reduced dimensionally to their corresponding midsurfaces for quicker and fairly accurate results of Computer-aided Engineering (CAE) analysis. Generation of the midsurface is still a time-consuming and mostly, a manual task due to lack of robust and automated techniques. Midsurface failures manifest in the form of gaps, overlaps, not-lying-halfway, etc., which can take hours or even days to correct. Most of the existing techniques work on the complex ﬁnal shape of the model forcing the usage of hard-coded heuristic rules, developed on a case-by-case basis. The research presented here proposes to address these problems by leveraging feature-parameters, made available by the modern feature-based CAD applications, and by effectively leveraging them for sub-processes such as simpliﬁcation, abstraction and
decomposition.
In the proposed system, at ﬁrst, features which are not part of the gross shape are removed from the input sheet metal feature-based CAD model. Features of the gross-shape model are then transformed into their corresponding generic feature equivalents, each having a proﬁle and a guide curve. The abstracted model is then decomposed into non-overlapping cellular bodies. The cells are classiﬁed into midsurface-patch generating cells, called ‘solid cells’ and patch-connecting cells, called ‘interface cells’. In solid cells, midsurface patches are generated either by offset or by sweeping the midcurve generated from the owner-feature’s proﬁle. Interface cells join all the midsurface patches incident upon them. Output midsurface is then validated for correctness. At the end, real-life parts are used to demonstrate the efﬁcacy of the approach.

**Category:** Geometry

[5] **viXra:1904.0359 [pdf]**
*submitted on 2019-04-18 15:46:35*

**Authors:** Antoine Balan

**Comments:** 1 page, written in english

We define a natural Ricci flow for connections over a Riemannian manifold.

**Category:** Geometry

[4] **viXra:1904.0328 [pdf]**
*submitted on 2019-04-16 10:22:17*

**Authors:** Ulrich E. Bruchholz

**Comments:** 5 Pages.

It is explained why the geometry of space-time, first found by
Rainich, is generally valid. The equations of this geometry,
the known Einstein-Maxwell equations, are discussed, and results
are listed. We shall see how these tensor equations can be solved.
As well, neutrosophics is more supported than dialectics. We shall
find even more categories than described in neutrosophics.

**Category:** Geometry

[3] **viXra:1904.0123 [pdf]**
*submitted on 2019-04-06 21:12:45*

**Authors:** Hiroshi Okumura

**Comments:** 3 Pages.

We generalize a problem in Wasan geometry involving an arbelos, and construct a self-similar circle pattern.

**Category:** Geometry

[2] **viXra:1904.0023 [pdf]**
*submitted on 2019-04-01 07:30:13*

**Authors:** Edgar Valdebenito

**Comments:** 3 Pages.

En esta nota mostramos dos cuestiones elementales de geometría.

**Category:** Geometry

[1] **viXra:1904.0019 [pdf]**
*submitted on 2019-04-01 09:08:00*

**Authors:** Antoine Balan

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

We define a 3-form over a spinorial manifold by mean of the curvature tensor and the Clifford multiplication.

**Category:** Geometry