We study area-stationary, or maximal, surfaces in the space L(H 3 ) of oriented geodesics of hyperbolic 3-space, endowed with the canonical neutral Kähler structure. We prove that every holomorphic curve in L(H 3 ) is a maximal surface. We then classify Lagrangian maximal surfaces Σ in L(H 3 ) and prove that the family of parallel surfaces in H 3 orthogonal to the geodesics γ ∈ Σ form a family of equidistant tubes around a geodesic.

We study 2-dimensional submanifolds of the space L(H 3 ) of oriented geodesics of hyperbolic 3-space, endowed with the canonical neutral Kähler structure. Such a surface is Lagrangian iff there exists a surface in H 3 orthogonal to the geodesics of .We prove that the induced metric on a Lagrangian surface in L(H 3 ) has zero Gauss curvature iff the orthogonal surfaces in H 3 are Weingarten: the eigenvalues of the second fundamental form are functionally related. We then classify the totally null surfaces in L(H 3 ) and recover the well-known holomorphic constructions of flat and CMC 1 surfaces in H 3 .

Let L be a Lagrangian submanifold of a pseudo-or para-Kähler manifold which is H-minimal, i.e. a critical point of the volume functional restricted to Hamiltonian variations. We derive the second variation of the volume of L with respect to Hamiltonian variations. We apply this formula to several cases. In particular we observe that a minimal Lagrangian submanifold L in a Ricci-flat pseudo-or para-Kähler manifold is H-stable, i.e. its second variation is definite and L is in particular a local extremizer of the volume with respect to Hamiltonian variations. We also give a stability criterion for spacelike minimal Lagrangian

We report a multimodal endoscopic system capable of performing both color and fast multispectral imaging in the spectral range 400-1000 nm. The system is based on a computer controllable tunable light source, which can be coupled with all types of endoscopes. Performance evaluation showed about 60% flat transmittance in almost all the operating wavelengths, at about 13 nm bandwidth per tuning step. With this system adapted to a thin hysteroscope, we also report, for the first time, spectral analysis of the endometrium and unsupervised/objective clustering of the spectra. We have implemented a method combining the k-means algorithm with the silhouette criterion for estimating the number of the distinguishable spectral classes that may correspond to different medical conditions of the tissue. It was found that there are five-well defined clusters of spectra, while preliminary clinical data seem to correlate well with the tissue pathology.

Let (Σ 1 , g 1 ) and (Σ 2 , g 2 ) be connected, complete and orientable Riemannian two manifolds. Consider the two canonical Kähler structures (and J is the canonical product complex structure. Thus for ǫ = 1 the Kähler metric G + is Riemannian while for ǫ = −1, G − is of neutral signature. We show that the metric G ǫ is locally conformally flat iff the Gauss curvatures κ(g 1 ) and κ(g 2 ) are both constants satisfying κ(g 1 ) = −ǫκ(g 2 ).We also give conditions on the Gauss curvatures for which every G ǫ -minimal Lagrangian surface is the product γ 1 × γ 2 ⊂ Σ 1 × Σ 2 , where γ 1 and γ 2 are geodesics of (Σ 1 , g 1 ) and (Σ 2 , g 2 ), respectively. Finally, we explore the Hamiltonian stability of projected rank one Hamiltonian G ǫ -minimal surfaces.