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Algebraic restrictions on geometric realizations of curvature models

Corey Dunn;  Zoë Smith — 2021

Archivum Mathematicum

We generalize a previous result concerning the geometric realizability of model spaces as curvature homogeneous spaces, and investigate applications of this approach. We find algebraic restrictions to realize a model space as a curvature homogeneous space up to any order, and study the implications of geometrically realizing a model space as a locally symmetric space. We also present algebraic restrictions to realize a curvature model as a homothety curvature homogeneous space up to even orders,...

Equivalence classes of Latin squares and nets in ℂ P 2

Corey Dunn;  Matthew Miller;  Max Wakefield;  Sebastian Zwicknagl — 2014

Annales de la faculté des sciences de Toulouse Mathématiques

The fundamental combinatorial structure of a net in ℂ P 2 is its associated set of mutually orthogonal Latin squares. We define equivalence classes of sets of orthogonal Latin squares by label equivalences of the lines of the corresponding net in ℂ P 2 . Then we count these equivalence classes for small cases. Finally we prove that the realization spaces of these classes in ℂ P 2 are empty to show some non-existence results for 4-nets in ℂ P 2 .

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