In this paper we study the Calabi diastasis function of Hermitian symmetric spaces. This allows us to prove that if a complete Hermitian locally symmetric space (M, g) admits a Kaehler immersion into a globally symmetric space (S, G) then it is globally symmetric and the immersion is injective. Moreover, if (S, G) is symmetric of a specified type (Euclidean, noncompact, compact), then (M, g) is of the same type. We also give a characterization of Hermitian globally symmetric spaces in terms of their diastasis function. Finally, we apply our analysis to study the balanced metrics, introduced by Donaldson, in the case of locally Hermitian symmetric spaces.

Calabi's diastasis function for Hermitian symmetric spaces

LOI, ANDREA
2006-01-01

Abstract

In this paper we study the Calabi diastasis function of Hermitian symmetric spaces. This allows us to prove that if a complete Hermitian locally symmetric space (M, g) admits a Kaehler immersion into a globally symmetric space (S, G) then it is globally symmetric and the immersion is injective. Moreover, if (S, G) is symmetric of a specified type (Euclidean, noncompact, compact), then (M, g) is of the same type. We also give a characterization of Hermitian globally symmetric spaces in terms of their diastasis function. Finally, we apply our analysis to study the balanced metrics, introduced by Donaldson, in the case of locally Hermitian symmetric spaces.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11584/94489
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 22
  • ???jsp.display-item.citation.isi??? 23
social impact