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H. C. Wang [16] investigated compact transformation groups on spheres with codimension one orbits, after the classification of transitive actions of compact connected Lie groups on spheres was done completely by D. Montgomery-H. Samelson [12], A. Borel [1] and others. In this paper we study similar problem on rational cohomology complex projective spaces. Let G be a compact connected Lie group and let M be a simply connect ed rational cohomology complex projective n-space on which G acts differ entiably with a codimension one orbit. The purpose of this paper is to classify such pairs (G, M) up to essentially isomorphism. Here we say that

Classification of compact transformation groups on cohomology complex projective spaces with codimension one orbits