• PART-II CHARACTERS OF NAGENDRAM G-SEMI SUB NEAR-FIELD SPACE OF A G-NEAR-FIELD SPACE OVER NEAR-FIELD

Abstract

In this manuscript we prove that every element of a compact, connected Nagendram G-semi sub near-field space of a   G-near-field space over near-field lies in some maximal torus of Nagendram G-semi sub near-field space.  Suppose we know that exp : g ® N is onto. Then, if g Î N, we see that g = exp X for some X Î g.  Now, NX is an abelian sub algebra  of g and therefore lies in a maximal abelian sub-algebra h. Then, exp h is a maximal torus in N containing g. To prove that exp is onto, we will appeal to familiar tools from Riemannian geometry.