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 Gk(V) is defined as the set of all subspaces W ⊂ V such that dim(W) = k. In the case of V = Rn, Gk(V) is the set of k-fl ats in Rn 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