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Title of Journal: J Geom

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Abbravation: Journal of Geometry

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Springer International Publishing

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10.1007/bf01428818

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1420-8997

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An axiomatic look at the ErdősTrost problem

Authors: Franz Kalhoff Victor Pambuccian
Publish Date: 2016/01/29
Volume: 107, Issue: 2, Pages: 379-385
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Abstract

The ErdősTrost problem can be formulated in the following way “If the triangle XY Z is inscribed in the triangle ABC—with X Y and Z on the sides BC CA and AB respectively—then one of the areas of the triangles BXZ CXY AY Z is less than or equal to the area of the triangle XY Z” There are many different solutions for this problem In this note we take up a very elementary proof due to Szekeres and deduce that the class of ordered translation planes is the level in the hierarchy of affine planes where the ErdősTrost statement still holds true We also look at the conditions an absolute plane needs to satisfy for the validity of the ErdősTrost statement

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Other Papers In This Journal:
  1. A New Class of Translation Planes Constructed by Hyper-regulus Replacement
  2. Propellers in Affine Cayley–Klein Planes
  3. On semi-parallel lightlike hypersurfaces of indefinite Kenmotsu manifolds
  4. Deformation of minimal surfaces with planar curvature lines
  5. Rakić duality principle in the almost Hermitian geometry
  6. On compact semisimple Lie groups as 2-plectic manifolds
  7. An Obata type result for the first eigenvalue of the sub-Laplacian on a CR manifold with a divergence-free torsion
  8. Linearly small elation quadrangles
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