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Centre de Recerca Matem`atica
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... This is a very important notion in foliation theory. To make it clear, let us give the main examples of such structures. 2.2. Lie foliations We say that F is a Lie G-foliation, if T is a Lie group G and γij are restrictions of left translations on G. Such foliation can also be defined by a 1-form ω ...
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Four-vector

In the theory of relativity, a four-vector or 4-vector is a vector in Minkowski space, a four-dimensional real vector space. It differs from a Euclidean vector in how its magnitude is determined. The transformations that preserve this magnitude are the Lorentz transformations, which include spatial rotations, boosts (a change by a constant velocity to another inertial reference frame), and temporal and spatial inversions. Regarded as a homogeneous space, the transformation group of Minkowski space is the Poincaré group, which adds to the Lorentz group the group of translations. The Lorentz group may be represented by 4×4 matrices.The article considers four-vectors in the context of special relativity. Although the concept of four-vectors also extends to general relativity, some of the results stated in this article require modification in general relativity.
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