Page 119 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 119
TOPICS IN COMPLEX AND QUATERNIONIC GEOMETRY (MS-74)
Geometry of Kato manifolds
Alexandra Iulia Otiman, aiotiman@mat.uniroma3.it
Università di Firenze, Italy
Coauthors: Nicolina Istrati, Massimiliano Pontecorvo, Matteo Ruggiero
Kato manifolds are compact complex manifolds containing a global spherical shell. Their mod-
ern study has been widely carried out in complex dimension 2 and originates in the seminal
work of Inoue, Kato, Nakamura and Hirzebruch.
In this talk I plan to describe a special class of Kato manifolds in arbitrary complex di-
mension, whose construction arises from toric geometry. I will present several of their analytic
and geometric properties, including existence of special complex submanifolds and partial re-
sults on their Dolbeault cohomology. Moreover, since they are compact complex manifolds of
non-Kähler type, I will investigate what special Hermitian metrics they support.
Semisimple Lie algebras and special Hermitian metrics
Fabio Podestà, fabio.podesta@unifi.it
Università degli Studi di Firenze, Italy
In this talk I will very shortly review some facts about invariant complex structures on semisim-
ple real non-compact Lie algebras and I will then discuss the existence and properties of special
invariant Hermitian metrics (such as balanced metrics) on compact quotients of real simple non
compact, even-dimensional groups.
On the continuation of quaternionic logarithm along curves and the
winding number
Jasna Prezelj, jasna.prezelj@fmf.uni-lj.si
UP FAMNIT/UL FMF/IMFM, Slovenia
Coauthors: Fabio Vlacci, Graziano Gentili
We present a continuation of the quaternionic logarithm along quaternionic curves. More pre-
cisely, given a continuous curve γ : [0, 1] → H \ {0}, we determine the geometric properties
of γ, which ensure that there exists a continuous curve γ˜ : [0, 1] → H with exp(γ˜(t)) = γ(t),
t ∈ [0, 1]. We denote the continuation by Log γ := γ˜. When Log γ exists, and γ is closed, we
define the winding number of the curve γ.
Stability of Einstein metrics
Uwe Semmelmann, uwe.semmelmann@mathematik.uni-stuttgart.de
Uni Stuttgart, Germany
Einstein metrics can be characterised as critical points of the (normalised) total scalar curvature
functional. They are always saddle points. However, there are Einstein metrics which are local
maxima of the functional restricted to metrics of fixed volume and constant scalar curvature.
117
Geometry of Kato manifolds
Alexandra Iulia Otiman, aiotiman@mat.uniroma3.it
Università di Firenze, Italy
Coauthors: Nicolina Istrati, Massimiliano Pontecorvo, Matteo Ruggiero
Kato manifolds are compact complex manifolds containing a global spherical shell. Their mod-
ern study has been widely carried out in complex dimension 2 and originates in the seminal
work of Inoue, Kato, Nakamura and Hirzebruch.
In this talk I plan to describe a special class of Kato manifolds in arbitrary complex di-
mension, whose construction arises from toric geometry. I will present several of their analytic
and geometric properties, including existence of special complex submanifolds and partial re-
sults on their Dolbeault cohomology. Moreover, since they are compact complex manifolds of
non-Kähler type, I will investigate what special Hermitian metrics they support.
Semisimple Lie algebras and special Hermitian metrics
Fabio Podestà, fabio.podesta@unifi.it
Università degli Studi di Firenze, Italy
In this talk I will very shortly review some facts about invariant complex structures on semisim-
ple real non-compact Lie algebras and I will then discuss the existence and properties of special
invariant Hermitian metrics (such as balanced metrics) on compact quotients of real simple non
compact, even-dimensional groups.
On the continuation of quaternionic logarithm along curves and the
winding number
Jasna Prezelj, jasna.prezelj@fmf.uni-lj.si
UP FAMNIT/UL FMF/IMFM, Slovenia
Coauthors: Fabio Vlacci, Graziano Gentili
We present a continuation of the quaternionic logarithm along quaternionic curves. More pre-
cisely, given a continuous curve γ : [0, 1] → H \ {0}, we determine the geometric properties
of γ, which ensure that there exists a continuous curve γ˜ : [0, 1] → H with exp(γ˜(t)) = γ(t),
t ∈ [0, 1]. We denote the continuation by Log γ := γ˜. When Log γ exists, and γ is closed, we
define the winding number of the curve γ.
Stability of Einstein metrics
Uwe Semmelmann, uwe.semmelmann@mathematik.uni-stuttgart.de
Uni Stuttgart, Germany
Einstein metrics can be characterised as critical points of the (normalised) total scalar curvature
functional. They are always saddle points. However, there are Einstein metrics which are local
maxima of the functional restricted to metrics of fixed volume and constant scalar curvature.
117
