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A minimal atlas for the rotation group SO(3). (English) Zbl 1226.22027

Summary: We describe explicitly an atlas for the rotation group SO(3) consisting of four charts where each chart is defined by Euler angles or each chart is defined by Cardan angles. This is best possible since it is well known that three charts do not suffice.

MSC:

22E70 Applications of Lie groups to the sciences; explicit representations
20H15 Other geometric groups, including crystallographic groups
53Z05 Applications of differential geometry to physics
57R55 Differentiable structures in differential topology
86A30 Geodesy, mapping problems
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