ETD

Digital archive of theses discussed at the University of Pisa

 

Thesis etd-04222016-144839


Thesis type
Tesi di laurea magistrale
Author
USULA, MARCO
URN
etd-04222016-144839
Thesis title
Kähler immersions into complex space forms
Department
MATEMATICA
Course of study
MATEMATICA
Supervisors
relatore Prof. Loi, Andrea
correlatore Prof. Frigerio, Roberto
Keywords
  • complex geometry
  • Kähler geometry
  • differential geometry
Graduation session start date
13/05/2016
Availability
Withheld
Release date
13/05/2086
Summary
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.
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