Geometry

1708 Submissions

[4] viXra:1708.0236 [pdf] submitted on 2017-08-19 17:45:13

Property of a Curve Connecting Any Two Points in Space that Are at Different Differences from a Third Point

Authors: Prashanth R. Rao
Comments: 1 Page.

Abstract: In this paper we prove that any two points A and B in space that are at different distances from a third point C, when connected by any curve in three dimensional space, must contain points such as D that are at intermediate distances from the third point C (length DC is intermediate to length AC and length BC).
Category: Geometry

[3] viXra:1708.0229 [pdf] submitted on 2017-08-19 12:49:36

Regarding Three Points in a Plane Such that Two Points Are Non-Equidistant from the Third Point and a Predicted Property of Any Curve in that Plane Connecting the Two Non-Equidistant Points

Authors: Prashanth R. Rao
Comments: 1 Page.

In this paper, we give a simple proof that if there are two points A and B that are at distinct linear distances from a third point C (AC is not equal to BC), then any curve connecting the points A and B (this curve lies within the same plane containing A,B,C) must contain points such as D that lie at an intermediate distance from C, (DC is of length intermediate to AC and BC).
Category: Geometry

[2] viXra:1708.0191 [pdf] submitted on 2017-08-17 03:54:59

A Derivation of the Ricci Flow

Authors: Vu B Ho
Comments: 6 Pages.

In this work we show that by restricting the coordinate transformations to the group of time-independent coordinate transformations it is possible to derive the Ricci flow from the contracted Bianchi identities.
Category: Geometry

[1] viXra:1708.0027 [pdf] submitted on 2017-08-02 13:40:27

The Quaternionic Manifolds

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

The pseudo-quaternionic manifolds are studied. Several tensors are defined.
Category: Geometry