# Liviu Ornea

3-7 October 2011 Liviu Ornea took part in conference Geometric structures on complex manifolds.

On

**May 10th 2013**he gave a talk "A survey of locally conformally Kaehler manifolds" at the seminar of the Laboratory.

Abstract: I shall introduce locally conformally Kaehler geometry and focus on examples, constructions, relations with other structures and topological properties.

On

**February 28th 2014**he gave a talk "Compact Homogeneous Locally Conformally Kaehler Manifolds" at the seminar of the Laboratory.

Abstract: 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.

On

**April 2014**Liviu Ornea gave a talk "Esential points of conformal vector fields".

Abstract: 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.

On April 2015 Liviu Ornea gave two talks:

"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.

On April 2017 года Liviu Ornea вgave a talk "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.

On October 4th 2019 Liviu Ornea gave a talk:

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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