Special Hermitian metrics on complex non-Kähler manifolds
Expositor: Daniele Angella (Università degli Studi di Firenze, Italia)
Resumen:
In the tentative to move from the Kähler to the non-Kähler setting, we consider several problems concerning Hermitian metrics on complex manifolds with special curvature properties and/or characterized by cohomological conditions.
We start by studying an analogue of the Yamabe problem for Hermitian manifolds. More precisely, we prove the existence of Hermitian metrics having constant scalar curvature with respect to the Chern connection when the expected curvature is non-positive, and we point out the difficulties in the positive curvature case. This problem relates also to several notions of Chern-Einstein metrics.
We also investigate symmetries of the curvature tensor of “canonical” connections of Hermitian manifolds. In particular, we focus on 6-dimensional Calabi-Yau solvmanifolds, namely, with trivial canonical bundle.
We finally provide some considerations in the locally conformally Kähler case, here including the investigation of lcK metrics induced by immersion into Hopf manifolds.
The talk is base on joint works with: Simone Calamai, Cristiano Spotti; Antonio Otal, Raquel Villacampa, Luis Ugarte; Michela Zedda.
We start by studying an analogue of the Yamabe problem for Hermitian manifolds. More precisely, we prove the existence of Hermitian metrics having constant scalar curvature with respect to the Chern connection when the expected curvature is non-positive, and we point out the difficulties in the positive curvature case. This problem relates also to several notions of Chern-Einstein metrics.
We also investigate symmetries of the curvature tensor of “canonical” connections of Hermitian manifolds. In particular, we focus on 6-dimensional Calabi-Yau solvmanifolds, namely, with trivial canonical bundle.
We finally provide some considerations in the locally conformally Kähler case, here including the investigation of lcK metrics induced by immersion into Hopf manifolds.
The talk is base on joint works with: Simone Calamai, Cristiano Spotti; Antonio Otal, Raquel Villacampa, Luis Ugarte; Michela Zedda.
Lugar: Aula 27, FaMAF
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