The geometry of sine-Laplace, sinh-Laplace equations

If M is a Riemannian manifold, i.e. the metric of M is positively definite, then the Euler equation of the energy integral is a system of nonlinear elliptic equations. If M is a Lorentzian manifold, then the Euler equation is a nonlinear hyperbolic system. The author discusses the problem of whether there exists a relationship between harmonic maps and the nonlinear elliptic equations. (Auth.)