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Self-Orthogonal Compact Spreads and Unitals in Topological Translation Planes

Authors:	Harald Löwe Rainer Löwen Emine Soytürk

Affiliation:	(1) Institut für Analysis, Technische Universität Braunschweig, Pockelsstr. 14, D-38106 Braunschweig, Germany.;(2) Institut für Analysis, Technische Universität Braunschweig, Pockelsstr. 14, D-38106 Braunschweig, Germany.;(3) Department of Mathematics, Faculty of Sciences, University of Ankara, 06100 Tandogan, Ankara, Turkey.

Abstract:	A spread of $V = mathbb{R}^{2l}$ is a set of l-dimensional subspaces L V partitioning V {0}. We construct examples of compact spreads that are identical with their sets of orthogonal spaces L. In the corresponding topological translation planes, every Euclidean sphere is a unital with the additional property that every point at infinity has flat feet.

Keywords:	topological translation plane comact spread unital flat feet
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