[geometry-ml:06617] 大阪大学幾何セミナー(12月15日)

[Masataka Iwai]

皆様

大阪大学の岩井雅崇です. 大阪大学幾何セミナーのご案内をいたします.

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日時:
2025年12月15日(月) 13:30--15:00

場所:
大阪大学理学部E404講義室(豊中キャンパス)

講演者:
Lucas Gomes (大阪大学)

タイトル:
Vaisman Solvmanifolds as Finite Quotients of Kodaira-Thurson Nilmanifolds

アブストラクト:
A locally conformally Kähler (LCK) metric is, as the name suggests, a
Hermitian metric on a complex manifold which is locally conformal to a
Kähler metric. This condition can be succinctly expressed by requiring
that for some closed 1-form θ one has dω=ω∧θ, where ω is the
fundamental form. The manifold is called Vaisman when θ is parallel.
Vaisman manifolds are closely related to Sasakian manifolds; in the
compact case, any Vaisman manifold can be described as the mapping
torus of a compact Sasakian manifold. In this talk, we discuss the
classification problem of Vaisman structures in the context of
solvmanifolds when the complex structure is not necessarily
left-invariant. In particular, we show that every Vaisman solvmanifold
is a finite quotient of the Kodaira-Thurston nilmanifold, extending
Bazzoni's result (2017) for Vaisman nilmanifolds and providing the
Vaisman analogue of Kasuya's result (2016) for Sasakian solvmanifolds.
Furthermore, we apply this characterization to extend a theorem of
Sawai (2017) on completely solvable solvmanifolds, to prove the
non-existence of LCK Einstein-Weyl structures on solvmanifolds, and to
show that Oeljeklaus–Toma manifolds admit no Vaisman structures.
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今後のセミナー予定表: http://www4.math.sci.osaka-u.ac.jp/sembbs2/announce.cgi
皆様のご参加をお待ちしております.

世話人：岩井雅崇, 濱中翔太, 松本佳彦（順不同）

大阪大学大学院理学研究科数学専攻
岩井雅崇
住所: 560-0043　大阪府豊中市待兼山町１-１
メールアドレス: masataka ＠ math.sci.osaka-u.ac.jp, masataka.math ＠ gmail.com,
iwai.masataka.sci ＠ osaka-u.ac.jp