On Surfaces in Three Dimensional Contact Manifolds

Locally Tame Curves and Surfaces in Three-dimensional Manifolds

Generalized Riemann minimal surfaces examples in three-dimensional manifolds products

In this paper, we construct and classify minimal surfaces foliated by horizontal constant curvature curves in M × R, where M is H, R or S. The main tool is the existence of a so called ”Shiffman” Jacobi field which characterize the property to be foliated in circles in these product manifolds.

Generalized Ricci Curvature Bounds for Three Dimensional Contact Subriemannian Manifolds

Measure contraction property is one of the possible generalizations of Ricci curvature bound to more general metric measure spaces. In this paper, we discover sufficient conditions for a three dimensional contact subriemannian manifold to satisfy this property.

On three dimensional stellar manifolds

It is well known that a three dimensional (closed, connected and compact) manifold is obtained by identifying boundary faces from a stellar ball a ⋆ S. The study of S/ ∼, two dimensional stellar sphere S with 2-simplexes identified in pairs leads us to the following conclusion: either a three dimensional manifold is homeomorphic to a sphere or to a stellar ball a⋆S with its boundary 2-simplexes...

On three-dimensional $N(k)$-paracontact metric manifolds and Ricci solitons

The aim of this paper is to characterize $3$-dimensional $N(k)$-paracontact metric manifolds satisfying certain curvature conditions. We prove that a $3$-dimensional $N(k)$-paracontact metric manifold $M$ admits a Ricci soliton whose potential vector field is the Reeb vector field $xi$ if and only if the manifold is a paraSasaki-Einstein manifold. Several consequences of this result are discuss...