2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/178073We study the geometry of M5-branes wrapping a 2-cycle which is Special Lagrangian with respect to a specific complex structure in a Calabi-Yau two-fold. Using methods recently applied to the three-fold case, we are again able find a characterization of the geometry, in terms of a non-integrable almost complex structure and a (2,0) form. This time, however, due to the hyper-K{ä}hler nature of the underlying 2-fold we also have the freedom of choosing a different almost complex structure with respect to which the wrapped 2-cycle is holomorphic. We show that this latter almost complex structure is integrable. We then relate our geometry to previously found geometries of M5-branes wrapping holomophic cycles and go further to prove some previously unknown results for M5-branes on holomorphic cycles.High Energy Physics - Theorytext