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Balanced metrics on complex vector bundles and the diastatic exponential of a symmetric space

Mossa, Roberto (2011) Balanced metrics on complex vector bundles and the diastatic exponential of a symmetric space. [Doctoral Thesis]

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Abstract

This thesis deals with two different subjects: balanced metrics on complex vector bundles and the diastatic exponential of a symmetric space. Correspondingly we have two main results. In the first one we prove that if a holomorphic vector bundle E over a compact Kähler manifold (M,ω) admits a ω-balanced metric then this metric is unique. In the second one, after defining the diastatic exponential of a real analytic Kähler manifold, we prove that for every point p of an Hermitian symmetric space of noncompact type there exists a globally defined diastatic exponential centered in p which is a diffeomorphism and it is uniquely determined by its restriction to polydisks.

Item Type:Doctoral Thesis
Date:13 January 2011
Tutor:Loi, Andrea
PhD classes:Ciclo 23 > Matematica e calcolo scientifico
Coordinator:D'Ambra, Giuseppina
Institution:Universita' degli Studi di Cagliari
Divisions:Dipartimenti (fino a dicembre 2011) > Dipartimento di Matematica e informatica
Subjects:Area 01 - Scienze matematiche e informatiche > MAT/03 Geometria
Uncontrolled Keywords:Kähler metrics, bounded symmetric domains, symplectic duality, Jordan triple systems, Bergman operator, balanced metric, balanced basis, holomorphic maps into grassmannians, moment maps
ID Code:573
Deposited On:22 Mar 2011 13:57

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