Let M be a real hypersurface of a complex space form with almost contact metric structure (φ, ξ, η, g). In this paper, we study real hypersurfaces in a complex space form whose structure Jacobi operator Rξ = R(·, ξ)ξ is ξ-parallel. In particular, we prove that the condition ∇ξRξ = 0 characterizes the homogeneous real hypersurfaces of type A in a complex projective space or a complex hyperbolic ...

We calculate the energy levels of two particles trapped in a harmonic potential. The actual two-body potential, assumed to be spherically symmetric, is replaced by a projective operator (non-local separable potential) to determine the energy levels in a closed form. This approach overcomes the limitations of the regularized Fermi pseudopotential when the characteristic length of the two-body in...

Much of the work currently occurring in the field of Quantum Interaction (QI) relies upon Projective Measurement. This is perhaps not optimal, cognitive states are not nearly as well behaved as standard quantum mechanical systems; they exhibit violations of repeatability, and the operators that we use to describe measurements do not appear to be naturally orthogonal in cognitive systems. Here w...

We calculate within an algebraic Bjorken–Johnson–Low (BJL) method anomalous Schwinger terms of fermionic currents and the Gauss law operator in chiral gauge theories. The current algebra is known to violate the Jacobi identity in an iterative computation. Our method takes the subtleties of the equal–time limit into account and leads to an algebra that fulfills the Jacobi identity. The non-itera...

Can eve.ry (non-Desarguest.. an) projee.,tJVe p~' ~ imbedded (in some natural, g~anet.ric ff.hion) in af1J8sarguesian) projective space? The Ite,titn is ne...WI~.ut .. ,trnp .. · ortant, for, if the answer is yes, tfo entirely SEijifia'Wt fields of research can be united~ 1his paper ;p~1des. conceptually simple geometric construction 1vh1dti',Y1elds an affirmative answer for a broad class of pl...

Lines classification is the central tool for visibility calculation in dimension n ≥ 2. It has been previously expressed in Grassmann Algebra, allowing to work with any couple of 2-vectors, which may represent two real lines or not. This article discusses about the nature of lines in the conformal model, searching if such a classification is still valid in Rn+1,1. First, it shows that the proje...

We investigate a projective limit space associated with an F2n unimodal mapping consisting of two hyperbolae. We show that in case n = 0 this limit is homeomorphic to an interval, in case n = 1 it is homeomorphic to sum of the interval {0}× [−1, 1] and the graph of the function sin 1 x , x ∈ [0, 1], and in case n = 3 it is a more complicated subspace of R3 endowed with a specific geometrical be...

The standard model fermion spectrum, including a right handed neutrino, can be obtained as a zero-mode of the Dirac operator on a space which is the product of complex projective spaces of complex dimension two and three. The construction requires the introduction of topologically non-trivial background gauge fields. By borrowing from ideas in Connes’ non-commutative geometry and making the com...

Let X be a compact Hausdorff space. We study finite-to-one map-pings r : X → X, onto X, and measures on the corresponding projective limit space X∞(r). We show that the invariant measures on X∞(r) correspond in a one-to-one fashion to measures on X which satisfy two identities. Moreover, we identify those special measures on X∞(r) which are associated via our correspondence with a function V on...