Achtdimensionale lokalkompakte Translationsebenen mit mindestens 17-dimensionaler Kollineationsgruppe

Ohne Zusammenfassung     

4-dimensionale Translationsebenen mit irreduzibler Kollineationsgruppe

Ohne Zusammenfassung     

Achtdimensionale lokalkompakte Translationsebenen mit großen Streckungsgruppen

Ohne Zusammenfassung     

4-dimensionale Translationsebenen mit 8-dimensionaler Kollineationsgruppe

Ohne Zusammenfassung     

Die Oktavenebene als Translationsebene mit großer Kollineationsgruppe

It is shown that the affine plane over the Cayley numbers is the only 16-dimensional locally compact topological translation plane having a collineation group of dimension at least 41. This (hitherto unpublished) result is one of the ingredients of H. Salzmann's characterizations of the Cayley plane among general compact projective planes by the size of its collineation group.The proof involves various case studies of the possibilities for the structure and size of collineation groups of 16-dimensional locally compact translation planes. At the same time, these case studies are important steps for a classification program aiming at the explicit determination of all such translation planes having a collineation group of dimension at least 38.     

Kompakte Ebenen mit einfacher Kollineationsgruppe

Ohne ZusammenfassungMeinem verehrten LehrerReinhold Baer zum 60. Geburtstag     

Steinersche Tripelsysteme mit fahnentransitiver Kollineationsgruppe

Ohne ZusammenfassungHerrnF. W. Levi zu seinem 75. Geburtstag gewidmet     

4-dimensionale Translationsebenen mit kommutativer Standgruppe

Ohne ZusammenfassungHerrn Günter Pickert zum 60. Geburtstag     

Translationsebenen der ordnung 49 mit scherungen

It is shown that there exists, up to isomorphism, exactly one non-Desarguesian translation plane of order 49 which admits non-trivial shears. Furthermore, the collineation groups of this plane and all its derived planes are described.     

Die Kollineationsgruppe verallgemeinerter André-Ebenen mit Homologien

Ohne Zusammenfassung     

4-Dimensionale Translationsebenen mit genau einer fixrichtung

Ohne Zusammenfassung     

Einige Eigenschaften von beliebigen Translationsebenen mit Scherungen

We study the automorphism-group of a not necessarily finite affine translation-plane the lines of which are all axes of non-trivial shears. We prove: Every reflection of the translation-plane can be represented as the product of three shears. Furthermore, the group which is generated by all shears is transitive on the set of lines of the translation-plane.In another section we consider conditions for such translationplanes to be Moufang-planes. One knows examples of finite planes with the above structure, which are not Moufang-planes and hence (as every Moufang-plane is already Desarguesian) not Desarguesian (Compare the results of 4],[6] and [7]).     

Zur Klassifikation von Salzmann-Ebenen mit dreidimensionaler Kollineationsgruppe

Ohne Zusammenfassung     

Kompakte,vier-dimensionale projektive Ebenen mit 8-dimensionaler Kollineationsgruppe

Ohne ZusammenfassungHerrn Hellmuth Kneser zum 75. Geburtstag am 16. 4. 1973 gewidmet     

Projektive Räume mit einer kommutativen transitiven Kollineationsgruppe

Ohne ZusammenfassungFrauRuth Moufang zum 60. Geburtstag am 10. Januar 1965 gewidmet     

A construction of Spin(7)-instantons

Joyce constructed examples of compact eight-manifolds with holonomy Spin(7), starting with a Calabi–Yau four-orbifold with isolated singular points of a special kind. That construction can be seen as the gluing of ALE Spin(7)-manifolds to each singular point of the Calabi–Yau four-orbifold divided by an anti-holomorphic involution fixing only the singular points. On the other hand, there are higher-dimensional analogues of anti-self-dual instantons in four dimensions on Spin(7)-manifolds, which are called Spin(7)-instantons. They are minimizers of the Yang–Mills action, and the Spin(7)-instanton equation together with a gauge fixing condition forms an elliptic system. In this article, we construct Spin(7)-instantons on the examples of compact Spin(7)-manifolds above, starting with Hermitian–Einstein connections on the Calabi–Yau four-orbifolds and ALE spaces. Under some assumptions on the Hermitian–Einstein connections, we glue them together to obtain Spin(7)-instantons on the compact Spin(7)-manifolds. We also give a simple example of our construction.     

Translationsebenen der Ordnung 49 mit einer Quaternionengruppe von Dehnungen

We show that there exist, up to isomorphism, exactly ten translation planes of order A9 which admit a quaternion group consisting of homologies with affine axis.