29 oct 2024 -- 16:15
Geometry in Como
Abstract.
In 1963, Morimoto proved that the product of two normal almost contact manifolds carries a natural complex structure. This result was later generalized by Watson and Tsukada in the 1980s, who independently presented a family of complex structures $J_{a,b}$ for $a,b\in\mathbb{R}$, $b\neq 0$, along with a family of compatible Riemannian metrics $g_{a,b}$. In this talk, we will investigate, in the case of a product $S_1\times S_2$ of two Sasakian manifolds, under which conditions the Hermitian structure $(J_{a,b},g_{a,b})$ has nice geometric properties which have been recently studied in the literature, specifically, whether it is Kähler, balanced, locally conformally Kähler, SKT, astheno-Kähler, or k-Gauduchon. Additionally, we will study the associated Bismut connection and construct new examples of Calabi-Yau with torsion manifolds beginning with a particular class of Sasakian manifolds known as $\eta-$Einstein manifolds.