The study of Einstein constraint equations in general relativity naturally leads to considering Riemannian manifolds equipped with nonsmooth metrics. There are several important differential operators on whose definitions depend the metric: gradient, divergence, Laplacian, covariant derivative, conformal Killing operator, and vector among others. In this article, we approximation such operators...

In this paper we give a positive answer to the open existence problem for complex-valued harmonic morphisms from the non-compact irreducible Riemannian symmetric spaces SLn(R)/SO(n), SU∗(2n)/Sp(n) and their compact duals SU(n)/SO(n) and SU(2n)/Sp(n). Furthermore we prove the existence of globally defined, complex-valued harmonic morphisms from any Riemannian symmetric space of type IV.

In a complete Riemannian manifold (M,g) if the hessian of a real valued function satisfies some suitable conditions then it restricts the geometry of (M,g). In this paper we characterize all compact rank-1 symmetric spaces, as those Riemannian manifolds (M,g) admitting a real valued function u such that the hessian of u has atmost two eigenvalues −u and − 2 , under some mild hypothesis on (M,g)...

This paper deals with a semi-classical limit(Theorem 1) by using traditional mathematical methods, and shows a Hopf theorem as a corollary. A formal discussing of it may be found in [7] 1 A semi-classical limit theorem Let M be a compact, closed Riemannian manifold of dim n, and V a vector field without degenerate zeros on M . Let Λ∗(M) be the space of differential forms on M , and D = d+ δ : Λ...