Geometry

1707 Submissions

[7] viXra:1707.0249 [pdf] submitted on 2017-07-18 12:52:38

Numerical Calculation of the Rainich Space in the Vicinity of a Singularty

Authors: Ulrich E. Bruchholz, Horst Eckardt
Comments: 19 Pages.

The well known numerical method of approximating differential quotients by quotients of differences is used in a novel context. This method is commonly underestimated, wrongly. The method is explained by an ordinary differential equation first. Then it is demonstrated how this simple method proves successful for non-linear field equations with chaotic behaviour. Using certain discrete values of their integration constants, a behaviour comparable with Mandelbrot sets is obtained. Instead of solving the differential equations directly, their convergence behaviour is analyzed. As an example the Einstein-Maxwell equations are investigated, where discrete particle quantities are obtained from a continuous theory, which is possible only by this method. The special set of integration constants contains values identical with particle characteristics. Known particle values are confirmed, and unknown values can be predicted. In this paper, supposed neutrino masses are presented.
Category: Geometry

[6] viXra:1707.0242 [pdf] submitted on 2017-07-17 13:20:25

The Folium of Descartes

Authors: Edgar Valdebenito
Comments: 4 Pages.

In this note we briefly examine the curve: x^3+y^3=sqrt(2)*x*y
Category: Geometry

[5] viXra:1707.0181 [pdf] submitted on 2017-07-12 20:58:33

14

Authors: Pan Zhang
Comments: 14 Pages.

Let $V$ be an asymptotically cylindrical K\"{a}hler manifold with asymptotic cross-section $\mathfrak{D}$. Let $E_\mathfrak{D}$ be a stable Higgs bundle over $\mathfrak{D}$, and $E$ a Higgs bundle over $V$ which is asymptotic to $E_\mathfrak{D}$. In this paper, using the continuity method of Uhlenbeck and Yau, we prove that there exists an asymptotically translation-invariant Hermitian projectively Hermitian Yang-Mills metric on $E$.
Category: Geometry

[4] viXra:1707.0046 [pdf] submitted on 2017-07-04 11:58:48

Complex Laplacian Operator

Authors: Antoine Balan
Comments: 2 pages, written in french

A Laplacian operator is defined bound to a riemannian manifold with a pseudo-complex structure.
Category: Geometry

[3] viXra:1707.0011 [pdf] submitted on 2017-07-01 08:14:34

Solution of Poincare's Vector Field Problem

Authors: John Atwell Moody
Comments: 17 Pages. written September 2014

When a meromorphic vector field is given on the projective plane, a complete holomorphic limit cycle, because it is a closed singular submanifold of projective space, is defined by algebraic equations. Also the meromorphic vector field is an algebraic object. Poincare had asked, is there just an algebraic calculation leading from the vector field to the defining equations of the solution, without the mysterious intermediary of the dynamical system. The answer is yes, that there is nothing more mysterious or wonderful that happens when a complete holomorphic limit cycle is formed than could have been defined using algebra.
Category: Geometry

[2] viXra:1707.0010 [pdf] submitted on 2017-07-01 08:17:31

Nine Notes on Modular Forms

Authors: John Atwell Moody
Comments: Pages.

Contents:

Analytic primality testing 1
Lefshetz numbers of modular curves 23
Grothendieck sections and rational points of modular curves 29
Rational points of modular curves 33
Conclusion about modular forms 41
Outline geometric proof of Mordell’s conjecture 48
Example:the Fermat curves
63 The residue calculation 69
The meaning of positive and negative 81


Category: Geometry

[1] viXra:1707.0009 [pdf] submitted on 2017-07-01 08:21:26

First Introduction to Toric Geometry

Authors: John Atwell Moody
Comments: Pages.

Contents

Projective toric varieties
Divisors
Maps
Chow ring
Fourier series and generalizations


Category: Geometry