Convex Bodies with Sheafs of Elliptic Sections

Abstract

<jats:p> A convex body in <jats:inline-formula> <jats:alternatives> <jats:tex-math notation="LaTeX">E^d</jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>E</mml:mi> <mml:mi>d</mml:mi> </mml:msup> </mml:mrow> </mml:math> </jats:alternatives> </jats:inline-formula> is an ellipsoid if all the sections given by hyperplanes are elliptic. We study whether we can restrict the hyperplanes to those that contain one of two fixed linear varieties. </jats:p>