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arXiv · 1710.02180

Kähler submanifolds in Iwasawa manifolds

Vasily Rogov
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Abstract

Iwasawa manifold is a compact complex homogeneous manifold isomorphic to a quotient of the group of complex unipotent $3 \times 3$ matrices by a cocompact lattice. We prove that any compact complex curve in an Iwasawa manifold is contained in a holomorphic torus. We also prove that any Kähler surface in an Iwasawa manifold is either an abelian surface or a non-projective isotrivial elliptic surface of Kodaira dimension one. In the Appendix we show that any complex torus in an Iwasawa manifold carries complex multiplication.

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Vasily Rogov. 2018-04-06. Kähler submanifolds in Iwasawa manifolds. https://arxiv.org/abs/1710.02180

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