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Klein
Klein geometries
plural of Klein geometry
Klein geometry
(differential geometry) A type of geometry (mathematical object representing a space and its spatial relationships); a homogeneous space X together with a symmetry group which represents the group action on X of some Lie group;
Klein paradoxes
plural of Klein paradox
Klein paradox
(quantum mechanics) A surprising result of applying the Dirac equation to the problem of electron scattering from a potential barrier. In non-relativistic quantum mechanics, electron tunnelling into a barrier is observed, with exponential damping. However, if the potential is of the order of the electron mass, V∼mc², the barrier is nearly transparent; moreover, as the potential approaches infinity, the reflection diminishes and the electron is always transmitted.
Klein quartics
plural of Klein quartic
Klein quadrics
plural of Klein quadric
Klein quadric
(mathematics) The lines of a 3-dimensional projective space, S, can be viewed as points of a 5-dimensional projective space, T. In that 5-space, the points that represent each line in S lie on a hyperbolic quadric, Q, known as the Klein quadric.
Klein quartic
(mathematics) A compact Riemann surface of genus 3 with the highest possible order automorphism group for this genus, namely order 168 orientation-preserving automorphisms, and 336 automorphisms if orientation may be reversed.