Liviu Ornea
3-7 октября 2011 года Liviu Ornea принял участие в международной конференции "Geometric structures on complex manifolds".
10 мая 2013 года он выступил на еженедельном семинаре Лаборатории с докладом "A survey of locally conformally Kaehler manifolds".
Аннотация: I shall introduce locally conformally Kaehler geometry and focus on examples, constructions, relations with other structures and topological properties.
28 февраля 2014 года он выступил на еженедельном семинаре Лаборатории с докладом "Compact Homogeneous Locally Conformally Kaehler Manifolds".
Аннотация: After a brief introduction on LCK manifolds and on the particular class of Vaisman manifolds, I shall prove that compact homogeneous LCK manifolds are Vaisman.
В апреле 2014 года Liviu Ornea выступил с докладом "Esential points of conformal vector fields".
Аннотация: An essential point of a conformal vector field X on a conformal manifold (M,c) is a point around which the local flow of X preserves no metric in the conformal class c. It is well-known that a conformal vector field vanishes at each essential point. We show that essential points are isolated. This is a generalization to higher dimensions of the fact that the zeros of a holomorphic function are isolated. As an application, we show that every connected component of the zero set of a conformal vector field is totally umbilical, thus generalizing a theorem of Kobayashi stating that the connected components of the zero set of a Killing field are totally geodesic. Based on joint work with F. Belgun and A. Moroianu.
В апреле 2015 года Liviu Ornea выступил с докладами:
"Zeros of conformal vector fields".
Abstract: The main result of this talk is that the essential zeros of a conformal vector field are isolated. This is then used to prove that the connected components of the zero set of a conformal vector field form a totally umbilical submanifold (i.e. in each normal direction, the second fundamental form is proportional to the metric), thus generalizing a result of S. Kobayashi about the zeros of Killing fields. This is joint work with F. Belgun and A. Moroianu
Charles Frances "Local Dynamics of Conformal Vector Fields" (arXiv: 0909.0044)
Charles Frances et Karin Melnick "Formers Normales pour les Champs Conformes pseudo-riemanniens" (arXiv: 1008.3781)
"On pluricanonical manifolds"
Abstract: A locally conformally Kaehler (LCK) manifold is a complex manifold which admits a covering with a Kaehler metric acted on through homotheties by the deck group. I describe a class of LCK manifolds, introduced by G. Kokarev and called pluricanonical, and prove they can be embedded in diagonal Hopf manifolds. Joint work with Misha Verbitsky.
В апреле 2017 года Liviu Ornea выступил с докладом:
"Recent results in locally conformally Kahler geometry"
Abstract: After a brief account on LCK geometry, with focus on LCK with potential and Vaisman manifolds, I shall describe several new results concerning compact LCK with potential, concerning their LCK rank and the fact that they contain Hopf surfaces.
4 октября 2019 г. Liviu Ornea выступил с докладом:
The Kahler geometry of the Weinstein construction
Abctract: We discuss the Weinstein construction of symplectic bundles in the framework of Kahler manifolds. In particular, we give examples of csc K"ahler metrics which are not Einstein-Kahler. We finally use the Weinstein construction to give a local characterization of Kahler manifolds admitting holomorphic, totally geodesic and homothetic foliations. This a joint work with Paul-Andi Nagy.
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