Let M be a simply connected complex submanifold of CN. We prove that M is irreducible, up a totally geodesic factor,if and only if the normal holonomy group acts irreducibly. This is an extrinsic analogue of the well-known De Rham decomposition theorem for a complex manifold. Our result is not valid in the real context, as it is shown by many counterexamples.

Reducibility of complex submanifolds of the complex euclidean spaces / DI SCALA, ANTONIO JOSE'. - In: MATHEMATISCHE ZEITSCHRIFT. - ISSN 0025-5874. - STAMPA. - 235:(2000), pp. 251-257. [10.1007/s002090000139]

Reducibility of complex submanifolds of the complex euclidean spaces

DI SCALA, ANTONIO JOSE'
2000

Abstract

Let M be a simply connected complex submanifold of CN. We prove that M is irreducible, up a totally geodesic factor,if and only if the normal holonomy group acts irreducibly. This is an extrinsic analogue of the well-known De Rham decomposition theorem for a complex manifold. Our result is not valid in the real context, as it is shown by many counterexamples.
File in questo prodotto:
File Dimensione Formato  
N02.pdf

accesso aperto

Tipologia: 2. Post-print / Author's Accepted Manuscript
Licenza: PUBBLICO - Tutti i diritti riservati
Dimensione 185.49 kB
Formato Adobe PDF
185.49 kB Adobe PDF Visualizza/Apri
Pubblicazioni consigliate

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/11583/1660756
 Attenzione

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