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The main results characterize Legendrian negative torus knots in every universally tight contact structure on Formula: see text. Together with Onaran and Min’s results, we obtain that in every universally tight contact structure on Formula: see text, Legendrian torus knots are determined by its classical invariants up to Legendrian isotopy. The main method is splitting Formula: see text by convex Heegaard decomposition.
Han Zhang (Wed,) studied this question.