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On Angles and Pseudo-Angles in Minkowskian Planes KU Leuven
© 2018 by the authors. The main purpose of the present paper is to well define Minkowskian angles and pseudo-angles between the two null directions and between a null direction and any non-null direction, respectively. Moreover, in a kind of way that will be tried to be made clear at the end of the paper, these new sorts of angles and pseudo-angles can similarly to the previously known angles be seen as (combinations of)Minkowskian lengths of ...
A link between torse-forming vector fields and rotational hypersurfaces KU Leuven
© 2017 World Scientific Publishing Company. Torse-forming vector fields introduced by Yano [On torse forming direction in a Riemannian space, Proc. Imp. Acad. Tokyo 20 (1944) 340-346] are natural extension of concurrent and concircular vector fields. Such vector fields have many nice applications to geometry and mathematical physics. In this paper, we establish a link between rotational hypersurfaces and torse-forming vector fields. More ...
On Chen Ideal Submanifolds Satisfying Some Conditions of Pseudo-symmetry Type KU Leuven
© Malaysian Mathematical Sciences Society and Universiti Sains Malaysia 2015. In this paper, we study Chen ideal submanifolds Mn of dimension n in Euclidean spaces 𝔼n+m (n ≥ 4, m ≥ 1) satisfying curvature conditions of pseudo-symmetry type of the form: the difference tensor R · C − C · R is expressed by some Tachibana tensors. Precisely, we consider one of the following three conditions: R·C −C · R is expressed as a linear combination of Q(g, R) ...
Curvature Properties of Some Class of Minimal Hypersurfaces in Euclidean Spaces KU Leuven
© 2015, University of Nis. All Rights Reserved. We determine curvature properties of pseudosymmetry type of some class of minimal 2-quasiumbilical hypersurfaces in Euclidean spaces En+1, n≥4. We present examples of such hypersurfaces. The obtained results are used to determine curvature properties of biharmonic hypersurfaces with three distinct principal curvatures in E5. Those hypersurfaces were recently investigated by Y. Fu in [38].
Psychology and Geometry I. On the geometry of the human kind KU Leuven
© 2015, University of Nis. All Rights Reserved. In this note an attempt is made to describe a personal look at some of the main steps in the history of geometry from a psychological point of view, hereby basing on and sometimes merely formulating again parts of some previous papers, like [1-11]. For general references on elementary differential geometry, pseudo Riemannian geometry and geometry of submanifolds, see e.g. [12-22]. In reference ...
A concise mini history of geometry: Leopold verstraelen KU Leuven
Mathematics was the crowning and lasting achievement of the ancient Greek culture. To more or less extent, arithmetical and geometrical problems had been explored already before, in several previous civilisations at various parts of the world, within a kind of practical mathematical scientific context. The knowledge which in particular as such first had been acquired in Mesopotamia and later on in Egypt, and the philosophical re ections on its ...
NOTES ON ISOTROPIC GEOMETRY OF PRODUCTION MODELS KU Leuven
The production function is one of the key concepts of mainstream neoclassical theories in economics. The study of the shape and properties of the production possibility frontier is a subject of great interest in economic analysis. In this respect, Cobb-Douglas and CES production functions with at graph hyper-surfaces in Euclidean spaces are first studied in [20, 21]. Later, more general studies of production models were given in [5]-[9] and [11, ...
Ricci and Casorati Principal Directions of Wintgen Ideal Submanifolds KU Leuven
© 2014, University of Nis. All rights reserved. We show that for Wintgen ideal submanifolds in real space forms the (intrinsic) Ricci principal directions and the (extrinsic) Casorati principal directions coincide.