Seminarium Teorii Względności i Grawitacji

We develop projective and conformal approaches to almost complex structures. Inboth cases, we replace the almost complex structure by a weighted analogue. Inthe conformal setting, using a certain canonical connection, we provide criteriacharacterising certain classes of the Gray-Hervella classification of almostHermitian manifolds, notably the class of semi-Kaehler manifolds, which includesnearly and almost Kaehler manifolds as special cases. Similar results can beobtained in projective geometry. Time permitting, I will also cover applicationsto conformal Patterson-Walker geometries. This is joint work with Josef Šilhan.