Invariant submanifolds of metric contact pairs
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- 作者：Amine Hadjar ; Paola Piu
- 关键词：Metric contact pair ; Minimal invariant submanifold ; Metric f ; structure ; Almost contact metric manifold
- 刊名：Annali di Matematica Pura ed Applicata (1923 -)
- 出版年：2017
- 出版时间：February 2017
- 年：2017
- 卷：196
- 期：1
- 页码：201-216
- 全文大小：
- 刊物类别：Mathematics and Statistics
- 刊物主题：Mathematics, general;
- 出版者：Springer Berlin Heidelberg
- ISSN：1618-1891
- 卷排序：196
文摘
We show that \(\phi \)-invariant submanifolds of metric contact pairs with orthogonal characteristic foliations make constant angles with the Reeb vector fields. Our main result is that for the normal case such submanifolds of dimension at least 2 are all minimal. We prove that an odd-dimensional \(\phi \)-invariant submanifold of a metric contact pair with orthogonal characteristic foliations inherits a contact form with an almost contact metric structure, and this induced structure is contact metric if and only if the submanifold is tangent to one Reeb vector field and orthogonal to the other one. Furthermore, we show that the leaves of the two characteristic foliations of the differentials of the contact pair are minimal. We also prove that when one Reeb vector field is Killing and spans one characteristic foliation, the metric contact pair is locally the product of a contact metric manifold with \({\mathbb {R}}\).