https://dspace.library.uu.nl/bitstream/handle/1874/17442/freudenthal_65_liegroups.pdf;sequence=1

Lie groups in the foundations of geometry

For the last decade there has been a generalized trend in mathematics on the search for large algebraic structures (linear spaces, closed subspaces, or infinitely generated algebras) composed of mathematical objects enjoying certain special properties. This trend has caught the eye of many researchers and has also had a remarkable influence in real and complex analysis, operator theory, summability theory, polynomials in Banach spaces, hypercyclicity and chaos, and general functional analysis. This expository paper is devoted to providing an account on the advances and on the state of the art of this trend, nowadays known as lineability and spaceability.

/pdf/linear-subsets-of-nonlinear-sets-in-topological-vector-3amm15jpk9.pdf

Linear subsets of nonlinear sets in topological vector spaces

Classification of concatenation measurement structures according to scale type

Compact Projective Planes

This chapter discusses isoparametric hypersurfaces and their generalizations The chapter presents a survey of isoparametric hypersurfaces, discusses Dupin hypersurfaces, and describes isoparametric submanifolds in ambient spaces that are finite dimensional Euclidean spaces or infinite dimensional Hilbert spaces The taut submanifolds in Riemannian manifolds are described The classification of isoparametric hypersurfaces in spheres with three principal curvatures is related to the various characterizations of the standard embeddings of the projective planes The chapter discusses isoparametric hypersurfaces in spheres with four different principal curvatures, all of which are assumed to have the same multiplicity The Clifford examples of Ferus, Karcher, and Munzner together with the homogeneous hypersurfaces are all known examples of isoparametric hypersurfaces in spheres A difference between isoparametric and Dupin hypersurfaces is that although the parallel hypersurfaces of the Dupin ones are also Dupin, they do not foliate the ambient space as the isoparametric ones do The hypersurface of a sphere is isoparametric if and only if it is equifocal

Chapter 10 - A Survey on Isoparametric Hypersurfaces and Their Generalizations

The aim of the Expositions is to present new and important developments in pure and applied mathematics. Well established in the community over more than two decades, the series offers a large library of mathematical works, including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers interested in a thorough study of the subject. Editorial Board Lev Birbrair, Universidade Federal do Ceara, Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany Katrin Wendland, University of Freiburg, Germany Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer, Mariusz Urbanski, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Bostjan Gabrovsek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)

Helmut Salzmann

Papers

Compact Projective Planes

Compact Projective Planes: With an Introduction to Octonion Geometry

Chapter 4 Compact projective planes

Topologische projektive ebenen

Kollineationsgruppen kompakter, vier-dimensionaler Ebenen