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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.
| Titolo: | Minimality of invariant submanifolds in metric contact pair geometry | |
| Autori: | ||
| Data di pubblicazione: | 2015 | |
| Rivista: | ||
| Handle: | http://hdl.handle.net/11584/87746 | |
| Tipologia: | 1.1 Articolo in rivista |
File in questo prodotto:
| File | Descrizione | Tipologia | Licenza | |
|---|---|---|---|---|
| invariant-submanifolds.pdf | versione post-print | Administrator Richiedi una copia |
http://hdl.handle.net/11584/87746
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