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On the generalization of Inoue manifolds
- Source :
- Pracì Mìžnarodnogo Geometričnogo Centru, Vol 13, Iss 4, Pp 24-39 (2020)
- Publication Year :
- 2020
- Publisher :
- Odessa National Academy of Food Technologies, 2020.
-
Abstract
- This paper is about a generalization of celebrated Inoue's surfaces. To each matrix M in SL(2n+1,ℤ) we associate a complex non-Kähler manifold TM of complex dimension n+1. This manifold fibers over S1 with the fiber T2n+1 and monodromy MT. Our construction is elementary and does not use algebraic number theory. We show that some of the Oeljeklaus-Toma manifolds are biholomorphic to the manifolds of type TM. We prove that if M is not diagonalizable, then TM does not admit a Kähler structure and is not homeomorphic to any of Oeljeklaus-Toma manifolds.
Details
- Language :
- Russian
- ISSN :
- 24098906 and 20729812
- Volume :
- 13
- Issue :
- 4
- Database :
- OpenAIRE
- Journal :
- Pracì Mìžnarodnogo Geometričnogo Centru
- Accession number :
- edsair.doi.dedup.....3a17379bfe749bc223058184975a0323