In this learning seminar series we will make an introduction to the locally conformally Kähler (LCK) geometry. A LCK metric is a structure on a complex manifold which falls somewhere between a Hermitian metric and a Kähler metric.

Ingredients of this weeks seminar is as follows:

   "Sasakian Metric"

We will be using the following resources.[5]

References:

1. S. Dragomir, L. Ornea - Locally conformal Kähler geometry.
   Progress in Mathematics, 155. Birkhäuser Boston, Inc., Boston, MA, 1998.


2. Vaisman, Izu. Some curvature properties of complex surfaces.
   Ann. Mat. Pura Appl. (4) 132 (1982), 1–18 (1983).


3. Vaisman, Izu. On locally and globally conformal Kähler manifolds.
   Trans. Amer. Math. Soc. 262 (1980), no. 2, 533–542.


4. Gauduchon, Paul. La 1-forme de torsion d'une variété hermitienne compacte.
   [Torsion 1-forms of compact Hermitian manifolds] Math. Ann. 267 (1984), no. 4, 495–518.


5. Falcitelli, Ianus, Pastore. Riemannian submersions and related topics.
   World Scientific Publishing Co., Inc., River Edge, NJ, 2004.


6. Şahin, B. Riemannian submersions, Riemannian maps in Hermitian geometry, and their applications.
   Elsevier/Academic Press, London, 2017.