Equi-isoclinic planes of Euclidean spaces

Lines on Planes in n-Dimensional Euclidean Spaces

The notation and terminology used here are introduced in the following papers: [1], [5], [12], [4], [9], [14], [13], [8], [15], [6], [2], [3], [7], [11], and [10]. We follow the rules: a, a1, a2, a3, b, b1, b2, b3, r, s, t, u are real numbers, n is a natural number, and x0, x, x1, x2, x3, y0, y, y1, y2, y3 are elements of R . One can prove the following propositions: (1) s t · (u · x) = s·u t ·...

Euclidean «-planes in Pseudo-euclidean Spaces and Differential Geometry of Cartan Domains

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...

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...

On Isometries of Euclidean Spaces