• complex geometry
• differential geometry
• Kähler geometry

In this thesis, we focus on holomorphic and isometric immersions of Kähler manifolds into complex space forms. Following a work of Calabi, we define a family of special Kähler potentials available in every analytic Kähler manifold, called diastatic potentials. They play an important role in studying holomorphic and isometric immersions of Kähler manifolds, because those immersions preserves diastatic potentials in the small. We prove Calabi's criterion, which explains when a Kähler manifold can be holomorphic and isometric immersed in a given complex space form of finite or infinite dimension. In the second part of the thesis, we provide some examples of application of Calabi's criterion, and following a work of Loi and Mossa, we use geometric quantization of Kähler manifolds to study holomorphic and isometric immersions of homogeneous Kähler manifolds into the complex projective space.