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Round fold maps are smooth maps on closed manifolds which are locallyrepresented as the product maps of Morse functions and identity maps on opendisks and whose singularity is realized as concentrically embedded spheres. Theauthor previously introduced such maps. Our paper presents round fold maps onsome $7$-dimensional simply-connected manifolds whose cohomology rings areisomorphic to that of the product of the $2$-dimensional complex projectivespace and a $3$-dimensional sphere. Such manifolds have been studied preciselyby Wang and round fold maps on spin manifolds in these manifolds have beenpreviously studied by the author. These manifolds form explicit classes ofhigehr dimensional closed and simply-connected manifolds, which are centralobjects in classical algeberic topology and differential topology.Understanding these manifolds in geometric and constructive ways is stillattractive, which we think as pioneers.  Fold maps are defined as smooth maps which are locally represented as theproduct maps of Morse functions and identity maps on open disks. They arefundamental and strong tools in generalizations of theory of Morse functionsand applications to geometry of manifolds. Explicit construction of fold mapsare difficult even on elementary or well-known manifolds whereas we can knowthe (non-)existence from Eliashberg's celebrating theory in the 1970s andrelated one in considerable cases.

Round fold maps into the plane on some $7$-dimensional closed and simply-connected manifolds