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Geometric structures on complex manifolds
October 7, 2011 15:00, Moscow
 


Maps that take lines to conics

Vladlen Timorin

HSE
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Vladlen Timorin


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Abstract: We will discuss generalizations of the classical theorem of Moebius (1827): a one-to-one self-map of a real projective space that takes all lines to lines is a projective transformation. E.g. we study sufficiently smooth local maps taking line segments to parts of conics. A description of local maps taking line segments to circle arcs depends non-trivially on the dimension (the descriptioninvolves classical geometries, quaternionic Hopf fibrations, representations of Clifford algebras). For most dimensions, it is still missing.

Language: English

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