Classification of torus manifolds with codimension one extended actions

Abstract

The purpose of this paper is to classify torus manifolds (M (2n) , T (n) ) with codimension one extended G-actions (M (2n) , G) up to essential isomorphism, where G is a compact, connected Lie group whose maximal torus is T (n) . For technical reasons, we do not assume torus manifolds are orientable. We prove that there are seven types of such manifolds. As a corollary, if a nonsingular toric variety or a quasitoric manifold has a codimension one extended action then such manifold is a complex projective bundle over a product of complex projective spaces.