A characterization of euclidean spaces

A Characterization of Euclidean Spaces

The purpose of this paper is to give an elementary proof of the fact that a Banach space in which there exist projection transformations of norm one on every two-dimensional linear subspace is a euclidean space. S. Kakutani [ l ] has pointed out that a modification of a proof due to Blaschke [2] will prove this theorem. F. Bohnenblust has been able to establish this theorem for the complex case...

A Characterization of Locally Euclidean Spaces

A Metric Characterization of Snowflakes of Euclidean Spaces

We give a metric characterization of snowflakes of Euclidean spaces. Namely, a metric space is isometric to Rn equipped with a distance (dE) , for some n ∈ N0 and ∈ (0, 1], where dE is the Euclidean distance, if and only if it is locally compact, 2-point isometrically homogeneous, and admits dilations of any factor.

A Characterization of Certain Conformally Euclidean Spaces of Class One

1. In this paper we will examine the metrics of conformally Euclidean spaces Cn (n^A) having the following two properties: (1) They are locally and isometrically imbeddable in Euclidean space of one higher dimension (£n+i), i.e. they are of class one. (2) With respect to a conformai coordinate system, the matrix of the second fundamental tensor [èy] has diagonal form. The condition for class on...

Spatial Analysis in curved spaces with Non-Euclidean Geometry

The ultimate goal of spatial information, both as part of technology and as science, is to answer questions and issues related to space, place, and location. Therefore, geometry is widely used for description, storage, and analysis. Undoubtedly, one of the most essential features of spatial information is geometric features, and one of the most obvious types of analysis is the geometric type an...