Research Areas
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Ruled surfaces, congruences of lines, and special complexes of lines have many applications
in kinematics and constructive geometry.
Line geometry is a natural higher-dimensional non-Euclidean geometry.
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Classical differential geometry deals with surfaces and curves in three-space and their
properties which can be described with the help of differential calculus.
Curvatures and curvature distributions on surfaces help to describe them.
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The triangle is sometimes considered to be the simplest geometric object in geometry.
However, there are stil so many open questions concerning the triangle in Euclidean planes as well as in
non-Euclidean planes.
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Generalizations of well-known Euclidean constructions to arbitrary geometries lead to new classes of curves.
Some questions from geometric optics result also result in new types of curves.
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Point models of various geometries allow us to treat complicated geometric objects as points.
This simplification needs higher-dimensional model spaces and have a lot of applications.
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Some surfaces arise in a natural way as set of points with certain properties.
We study singularities, metric, differential, and projective properties.
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Poncelet porisms of various forms bear a lot of algebraic problems.
Many phenomena can easily be observed with dynamic geometry software
and lead to a lot of conjectures, but
their verification need a lot of tricky manipulations.
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