# 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