In this paper, the geometry of invariant submanifolds of a Sasakian manifold are studied. Necessary and sufficient conditions are given on an submanifold of a Sasakian manifold to be invariant submanifold and the invariant case is considered. In this case, we investigate further properties of invariant submanifolds of a Sasakian manifold. M.S.C. 2000: 53C42, 53C15.

Let M0 be a compact, regular q-pseudoconcave compact CR submanifold of a complex manifold G and B a holomorphic vector bundle on G such that dimH ( M0,B ∣∣ M ) = 0 for some fixed r < q. We prove a global homotopy formula with C estimates for r-cohomology of B on arbitrary CR submanifold M close enough to M0.

We study the forms of curvatures of lightlike hypersurfaces M of an indefinite Kenmotsu manifold M̄ subject to the conditions: (1) M is locally symmetric, i.e., the curvature tensor R of M be parallel on TM , or (2) M is a semi-symmetric manifold, i.e., R(X, Y )R = 0 on TM . M.S.C. 2010: 53C25, 53C40, 53C50.

This paper discusses a 7 dimensional conformal geometric algebra model for spacetime based on the notion that spacelike and timelike infinities are distinct. I show how naturally of the dimensions represents the lightlike infinity and appears redundant in computations, yet usefull in interpretation.

We present a compact analytic formula for the two-loop six-particle maximally helicity violating remainder function (equivalently, the two-loop lightlike hexagon Wilson loop) in N=4 supersymmetric Yang-Mills theory in terms of the classical polylogarithm functions Lik with cross ratios of momentum twistor invariants as their arguments. In deriving our formula we rely on results from the theory ...

The geometry and topology of complete nonorientable maximal surfaces with lightlike singularities in the Lorentz-Minkowski 3-space is studied. Some topological congruence formulae for surfaces of this kind are obtained. As a consequence, some existence and uniqueness results for maximal Möbius strips and maximal Klein bottles with one end are proved.

We study the geometry of compact Lorentzian manifolds that admit a somewhere timelike Killing vector field, and whose isometry group has infinitely many connected components. Up to a finite cover, such manifolds are products (or amalgamated products) of a flat Lorentzian torus and a compact Riemannian (resp., lightlike) manifold.

We review the evidence for and against the possibility that the inner singularity of a black hole contains a lightlike segment which is locally mild and characterized by mass inflation. Submitted to: Physical Review Letters Permanet address: Institute of Astronomy, University of Catania, Viale Andrea Doria 5, 95125 Catania, Italy

This report discusses some results on differential cross sections for high energy and small momentum transfer elastic hadron-hadron scattering in QCD, using a functional integral approach. In particulary a matrix cumulant expansion for the vacuum expectation values of lightlike Wegner-Wilson loops, which governs the hadronic amplitudes, is presented. The cumulants are evaluated using the model ...

In this study, some identities involving the Riemannian curvature invariants are presented on lightlike hypersurfaces of a statistical manifold in Lorentzian settings. Several inequalities characterizing obtained. These also investigated space forms.