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On the nonexistence
of $S^6$ type complex threefolds in any compact homogeneous
complex manifolds with the compact lie group $G_2$ as the
base manifold
Daniel Guan |
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Vol. 305 (2020), No. 2, 641–644
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DOI: 10.2140/pjm.2020.305.641
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Abstract |
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In a recent preprint Professor Etesi asked a question: could one find a complex three dimensional submanifold in a compact complex seven dimensional homogeneous space with the compact real dimensional Lie group as the base manifold, such that is diffeomorphic to the six dimensional sphere ? We apply a result of Tits on compact complex homogeneous space, or of H. C. Wang and Hano–Kobayashi on the classification of compact complex homogeneous manifolds with a compact reductive Lie group to give an answer to his question. In particular, we show that one could not obtain a complex structure of in his way. |
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Keywords
complex structure, six dimensional sphere, cohomology,
invariant structure, complex torus bundles, Hermitian
manifolds
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Mathematical Subject Classification 2010
Primary: 53C15
Secondary: 57S25, 53C30, 22E99, 15A75
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Milestones
Received: 31 May 2019
Revised: 28 August 2019
Accepted: 7 November 2019
Published: 29 April 2020
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Authors |
| Daniel Guan | |
| School of Mathematics and
Statistics Henan University Kaifeng China |
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