The linear independence of sets of two and three canonical algebraic curvature tensors.
Algebraic restrictions on geometric realizations of curvature models
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
The fundamental combinatorial structure of a net in 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 . Then we count these equivalence classes for small cases. Finally we prove that the realization spaces of these classes in are empty to show some non-existence results for 4-nets in .
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