On the generalization of Inoue manifolds
2020 ◽
Vol 13
(4)
◽
pp. 24-39
Keyword(s):
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.
Keyword(s):
2002 ◽
pp. 263-299
Keyword(s):
1993 ◽
Vol 29
(1)
◽
pp. 111-114
1971 ◽
Vol 78
(4)
◽
pp. 342-351
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