Sasakian流形的部分全实子流形

中文摘要 AI 辅助

部分全实（PTR）子流形是在Kähler几何中通过区分全实分布并让其正交补不受限制而引入的。本文针对切于Reeb向量场的Sasakian流形的子流形，发展了相应的框架。在分离Reeb方向后，我们定义了全实分布和模糊分布，并证明反不变子流形、接触CR子流形、半斜子流形和逐点半斜子流形都是Sasakian PTR框架的特殊情况。我们建立了基本的切向和法向分解，研究了极大性和可积性，并推导了Reeb场产生的额外限制。随后，我们研究了典范态射P和F、相关分布的几何以及Sasakian空间形式中的PTR子流形，还包含了明确的模型以说明主要结构及其与Kähler情形的差异。

英文摘要

Partially totally real (PTR) submanifolds were introduced in Kähler geometry by distinguishing a totally real distribution and leaving its orthogonal complement unrestricted. In this paper we develop the corresponding framework for submanifolds of Sasakian manifolds tangent to the Reeb vector field. After separating the Reeb direction, we define the totally real and ambiguous distributions and show that anti-invariant, contact CR, hemi-slant and pointwise hemi-slant submanifolds occur as special cases of the Sasakian PTR framework. We establish the basic tangential and normal decompositions, study maximality and integrability, and derive the additional restrictions produced by the Reeb field. We then investigate the canonical morphisms \(P\) and \(F\), the geometry of the associated distributions, and PTR-submanifolds in Sasakian space forms. Explicit models are included to illustrate the principal structures and the differences from the Kähler case.

发表机构

• Kyungpook National University（庆北国立大学）
• Gyeongsang National University（庆尚国立大学）

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