On almost-analytic vectors in almost-Kählerian manifolds
On almost-analytic vectors in almost-Kählerian manifolds
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关于准凯勒流形中的准解析向量
DOI：
10.2748/tmj/1178244584
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发表时间：
1959
影响因子：
0.5
通讯作者：
S. Tachibana
中科院分区：
文献类型：
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作者：
S. Tachibana
在伪卡勒流形中，许多关于逆变或协变伪解析向量的有趣结果是已知的。尽管关于伪卡勒流形的论文很多，但关于准卡勒流形的论文却很少。最近，M. Apte 将博赫纳定理推广到紧致近卡勒流形。他的作品对我来说似乎很有启发。在本文中，我们将把伪卡勒流形中的几个定理推广到准卡勒流形。主要结果是紧近卡勒流形中向量场的积分公式。在第 1 节和第 2 节中，我们将准备恒等式和引理，并在第 3 节和第 4 节中定义几乎解析向量，它们是伪解析向量的概括。作为§5中积分公式的应用，我们将得到§6中的几个定理。在第 7 节中，我们将给出紧准卡勒-爱因斯坦流形中逆变准解析向量的李代数的分解定理。规范联系将在第 8 节中介绍，在最后一节中，对于逆变几乎解析向量，我们将推广 Apte 定理。
In pseudo-Kahlerian manifolds, many interesting results concerning contravariant or covariant pseudo-analytic vectors are known. Even though there were many papers about pseudo-Kahlerian manifolds, but were few about almost-Kahlerian ones. Recently, M. Apte generalized Bochner's theorem to compact almost-Kahlerian manifolds. His work seems to be very suggestive for me. In the present paper we shall generalize several theorems in pseudoKahlerian manifolds to almost-Kahlerian ones. The main results are integral formulas on vector fields in compact almost-Kahlerian manifolds. In §1 and §2 we shall prepare identities and lemmas and in §3 and §4 define almost-analytic vectors which are generalizations of pseudo-analytic vectors. As applications of integral formulas in §5, we shall obtain several theorems in §6. In §7, we shall give a decomposition theorem of the Lie algebra of contravariant almost-analytic vectors in a compact almost-Kahler-Einstein manifold. The canonical connection will be introduced in §8 and in the last section, to contravariant almost-analytic vectors, we shall generalize Apte's theorem.