On Some Results Of Harmonic Morphisms Between Semi-euclidean Spaces

In this thesis , we study harmonic morphisms betweem semi-Euclidean spaces R~ ? R~. We prove following two theorems which give two ways to construct harmonic morphisms between semi-Euclidean spaces, thus gen- eralize the corresponding results in [12] and [14]. We also give some inter- esting examples of quadratic harmonic morphims between semi-Euclidean spaces Theorem 2.3 be a harmonic morphism defined by homogeneous polynomial 01 degree ~ , tnen tne corn p.Lere UIL 01 9, uenneu is a harmonic morphism, where R~ x R~ is given the product metric having the form Theorem 2.4 be two harmonic morDhisrns. then the direct sum is a harmonic mor phism,where the product manifold MJ~ x is provided with the product metric...