Let G=SO(m+1) , m \geq 2, act in the standard way on S^m.
Let F:S^m \to S^m be a G-equivariant map, i.e., g F(g^{-1}x) =F(x) for all x \in S^m and g \in G.
Question 1: Is F the identity map?
If the answer is negative: Is F an isometry?
SO(m+1)-equivariant maps from S^m to S^m
Andrea Ratto
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