Abstract
In [5] we gave examples of triples of smooth functions to construct smooth -actions on the projective space whose restricted -action is the standard action. By using these examples of triples , we shall construct smooth (resp. analytic) -actions on whose restricted -action is the standard action. Consequently, we shall show that for each positive integer there exist uncountably infinite smooth conjugacy classes of smooth -actions on with closed and open orbits whose restricted -action is the standard action. On the other hand, we shall show that there exist exactly countably many analytic conjugacy classes of analytic -actions on with one closed and two open orbits whose restricted -action is the standard action.
Citation
Tomoaki ONO. "A Note on Equivalence Classes of -actions on whose Restricted -action is the Standard Action." Tokyo J. Math. 45 (2) 433 - 450, December 2022. https://doi.org/10.3836/tjm/1502179370
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