# Geometry

## 1008 Submissions

[5] **viXra:1008.0081 [pdf]**
*submitted on 28 Aug 2010*

### Smarandache's Minimum Theorem in the Einstein Relativistic Velocity Model of Hyperbolic Geometry

**Authors:** Catalin Barbu

**Comments:** 3 pages

In this note, we present a proof to the Smarandache's Minimum Theorem in the Einstein
Relativistic Velocity Model of Hyperbolic Geometry.

**Category:** Geometry

[4] **viXra:1008.0043 [pdf]**
*submitted on 16 Aug 2010*

### Differentiable Structures on Real Grassmannians

**Authors:** Jeidsan A. C. Pereira

**Comments:** 10 Pages.

Given a vector space V of dimension n and a natural number k < n, the
grassmannian G_{k}(V) is defined as the set of all subspaces W ⊂ V such that
dim(W) = k. In the case of V = R^{n}, G_{k}(V) is the set of k-fl
ats in R^{n} and
is called real grassmannian [1]. Recently the study of these manifolds has
found applicability in several areas of mathematics, especially in Modern
Differential Geometry and Algebraic Geometry. This work will build two
differential structures on the real grassmannian, one of which is obtained as a
quotient space of a Lie group [1], [3], [2], [7]

**Category:** Geometry

[3] **viXra:1008.0037 [pdf]**
*submitted on 12 Aug 2010*

### A Direct Proof of the Yff's Conjecture

**Authors:** Marian Dincă

**Comments:** 2 Pages.

In this paper it is given proof Yff's conjecture using convexity arguments.

**Category:** Geometry

[2] **viXra:1008.0031 [pdf]**
*submitted on 11 Aug 2010*

### Another Proof of a Theorem Relative to the Orthological Triangles

**Authors:** Ion Pătraşcu, Florentin Smarandache

**Comments:** 3 pages

In [1] we proved, using barycentric coordinates, the following theorem

**Category:** Geometry

[1] **viXra:1008.0030 [pdf]**
*submitted on 11 Aug 2010*

### Proof Wolstenholme-Lenhard Ciclic Inequality for Real Numbers and L.fejes Tóth Conjecture

**Authors:** Marian Dincă

**Comments:** 4 Pages.

In this paper an elementary proof of the Wolstenholme-Lenhard ciclic
inequality for real numbers and L.Fejes T&oactute;th conjecture( equivalent by Erdis-Mordell
inequality for polygon) is given, using a remarcable identity
We give the following:

**Category:** Geometry