Minimality of invariant submanifolds in metric contact pair geometry
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- 作者：Gianluca Bande ; Amine Hadjar
- 关键词：Contact pair ; Vaisman manifold ; Invariant submanifold ; Minimal submanifold ; Primary 53C25 ; Secondary 53B20 ; 53D10 ; 53B35 ; 53C12
- 刊名：Annali di Matematica Pura ed Applicata
- 出版年：2015
- 出版时间：August 2015
- 年：2015
- 卷：194
- 期：4
- 页码：1107-1122
- 全文大小：473 KB
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Amine Hadjar (2)
1. Dipartimento di Matematica e Informatica, Universit脿 degli Studi di Cagliari, Via Ospedale 72, 09124, Cagliari, Italy
2. Laboratoire de Math茅matiques, Informatique et Applications, Universit茅 de Haute Alsace, 4 Rue des Fr猫res Lumi猫re, 68093, Mulhouse, France - 刊物类别：Mathematics and Statistics
- 刊物主题：Mathematics
Mathematics - 出版者：Springer Berlin / Heidelberg
- ISSN：1618-1891
文摘
We study invariant submanifolds of manifolds endowed with a normal or complex metric contact pair with decomposable structure tensor \(\phi \). For the normal case, we prove that a \(\phi \)-invariant submanifold tangent to a Reeb vector field and orthogonal to the other one is minimal. For a \(\phi \)-invariant submanifold \(N\) everywhere transverse to both the Reeb vector fields but not orthogonal to them, we prove that it is minimal if and only if the angle between the tangential component \(\xi \) (with respect to \(N\)) of a Reeb vector field and the Reeb vector field itself is constant along the integral curves of \(\xi \). For the complex case (when just one of the two natural almost complex structures is supposed to be integrable), we prove that a complex submanifold is minimal if and only if it is tangent to both the Reeb vector fields.