Special Hermitian structures on products of Sasakian manifolds

Abstract: It is known that the product of two Sasakian manifolds carries a 2-parameter family of Hermitian structures $(J_{a,b},g_{a,b})$. In this talk we will investigate when these Hermitian structures are locally conformally Kähler, balanced, strong Kähler with torsion, Gauduchon or $k$-Gauduchon ($k≥2$). Moreover, we will study the Bismut connection associated to $(J_{a,b},g_{a,b})$ and we will provide formulas for the associated Bismut-Ricci tensor $\operatorname{Ric}^B$ and the Bismut-Ricci form $\rho^B$. We will show that these tensors vanish if and only if each Sasakian factor is $\eta$-Einstein with appropriate constants and we will also exhibit some examples fulfilling these conditions, thus providing new examples of Calabi-Yau with torsion manifolds. This talk is based in a recent joint work with my PhD advisor Adrián Andrada.

differential geometry

Audience: researchers in the topic

( paper | video )

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Virtual seminar on geometry with symmetries

Series comments: Description: Research seminar in Lie group actions in Riemannian geometry.

The seminar meets every other Wednesday. To accommodate most time zones, the time rotates. The Zoom link is sent to the mailing list around 24 hours before each talk. To subscribe to the mailing list, send a message to geometrywithsymmetries@gmail.com requiring it.

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