Minimality of invariant submanifolds in Metric Contact Pair Geometry

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 201

η\eta-Einstein Sasakian immersions in non-compact Sasakian space forms

The aim of this paper is to study Sasakian immersions of (non-compact) complete regular Sasakian manifolds into the Heisenberg group and into $\mathbb{B}^N\times \mathbb{R}$ equipped with their standard Sasakian structures. We obtain a complete classification of such manifolds in the $\eta$-Einstein case.Comment: To appear on Annali di Matematica Pura ed Applicata, minor corrections. arXiv admin note: text overlap with arXiv:1810.0077

η-Einstein Sasakian immersions in non-compact Sasakian space forms

The aim of this paper is to study Sasakian immersions of (non-compact) complete regular Sasakian manifolds into the Heisenberg group and into BN× R equipped with their standard Sasakian structures. We obtain a complete classification of such manifolds in the η-Einstein case

On normal contact pairs

We consider manifolds endowed with a contact pair structure. To such a structure are naturally associated two almost complex structures. If they are both integrable, we call the structure a normal contact pair. We generalize the Morimoto's Theorem on product of almost contact manifolds to flat bundles. We construct some examples on Boothby--Wang fibrations over contact-symplectic manifolds. In particular, these results give new methods to construct complex manifolds