20 research outputs found
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 . For the normal
case, we prove that a -invariant submanifold tangent to a Reeb vector
field and orthogonal to the other one is minimal. For a -invariant
submanifold 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 (with respect to ) of a Reeb vector
field and the Reeb vector field itself is constant along the integral curves of
. 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
-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 equipped with their standard Sasakian
structures. We obtain a complete classification of such manifolds in the
-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
Jin, J. E.; Park, J. H.; Sekigawa, K., Notes on some classes of 3-dimensional contact metric manifolds.
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