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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Summer 2018 • Question 3

Question

Math 6510 • Differentiable Manifolds Summer 2018 • Question 3

Let the inclusion of \(\SO (2)\) into \(\SO (3)\) be induced by the inclusion of \(\mathbb {R}^2\) into \(\mathbb {R}^3\). Find all connected, 2-dimensional Lie subgroups of \(\SO (3)\) that contain \(\SO (2)\).

Raw LaTeX

Let the inclusion of \(\SO(2)\) into \(\SO(3)\) be induced by the inclusion of
\(\R^2\) into \(\R^3\). Find all connected, 2-dimensional Lie subgroups of \(\SO(3)\)
that contain \(\SO(2)\).

Topic Tags

Lie Groups and Matrix Lie Groups