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EnglishWe study invariant submanifolds of manifolds endowed with a normal or complex metric contact pair with decomposable structure tensor $$\phi $$ϕ. For the normal case, we prove that a $$\phi $$ϕ-invariant submanifold tangent to a Reeb vector field and orthogonal to the other one is minimal. For a $$\phi $$ϕ-invariant submanifold $$N$$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 $$\xi $$ξ (with respect to $$N$$N) of a Reeb vector field and the Reeb vector field itself is constant along the integral curves of $$\xi $$ξ. 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.
Minimality of invariant submanifolds in metric contact pair geometry / Bande, Gianluca; Hadjar, Amine. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - 194:4(2015), pp. 1107-1122.
| Titolo: | Minimality of invariant submanifolds in metric contact pair geometry |
| Autori: | |
| Data di pubblicazione: | 2015 |
| Rivista: | |
| Citazione: | Minimality of invariant submanifolds in metric contact pair geometry / Bande, Gianluca; Hadjar, Amine. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - 194:4(2015), pp. 1107-1122. |
| Handle: | http://hdl.handle.net/11584/87746 |
| Tipologia: | 1.1 Articolo in rivista |
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http://hdl.handle.net/11584/87746
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