Minimality of invariant submanifolds in Metric Contact Pair Geometry
| Autor: | Bande, Gianluca, Hadjar, Amine |
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| Rok vydání: | 2014 |
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| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s10231-014-0412-8 |
| Popis: | We study invariant submanifolds of manifolds endowed with a normal or complex metric contact pair with decomposable endomorphism field $\phi$. 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. Comment: To appear in "Ann. Mat. Pura Appl. (4)", March 2014 |
| Databáze: | arXiv |
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