Properties of the Cauchy–Riemann–Fueter equation for maps between quaternionic manifolds are studied. Spaces of solutions in case of maps from a K3–surface to the cotangent bundle of a complex projective space are computed. A relationship between harmonic spinors of a generalized nonlinear Dirac operator and solutions of the Cauchy– Riemann–Fueter equation are established.

We analyze the excitons states in a quantum wire under intense laser radiation. Electrons and holes are confined by the parabolic potential of the quantum wire. An exactly solvable model is introduced for calculating the exciton binding energy, replacing the actual Coulomb interaction between the electron and the hole by a projective operator.

Using the methods of moving frames, we study real hypersurfaces in complex projective space CP and complex hyperbolic space CH whose structure Jacobi operator has various special properties. Our results complement work of several other authors who worked in CPn and CHn for n ≥ 3.

We propose a generalization of the classical theta function to higher cohomology of the polarization line bundle on a family of complex tori with positive index. The constructed cocycles vary horizontally with respect to the (projective) flat connection on this family coming from a heat operator. They also possess modular properties similar to the classical ones.

A Hermite type formula is introduced and used to study the zeta function over the real and complex n-projective space. This approach allows to compute the residua at the poles and the value at the origin as well as the value of the derivative at the origin, that gives the regularized determinant of the associated Laplacian operator.

We develop global pluripotential theory in the setting of Berkovich geometry over a trivially valued field. Specifically, we define and study functions measures finite energy non-Archimedean Monge–Ampère operator on any (possibly reducible) projective variety. also investigate topology space valuations linear growth, behavior plurisubharmonic thereon.

Part I introduced the notion of the projective linking number LinkP(Γ, Z) of a compact oriented real submanifold Γ of dimension 2p− 1 in complex projective n-space P with an algebraic subvariety Z ⊂ P−Γ of codimension p. It is shown here that a basic conjecture concerning the projective hull of real curves in P implies the following result: Γ is the boundary of a positive holomorphic p-chain of...