We 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

#### Abstract

We 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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11584/87746