24 citations · 171 across the 71 of their papers we have counts for
13 papers · 1 filter
Round fold maps of n--dimensional manifolds into
Naoki Kitazawa, Osamu Saeki
We determine those smooth --dimensional closed manifolds with which admit round fold maps into , i.e.\ fold maps whose critical value sets consist…
On Reeb graphs induced from smooth functions on 3-dimensional closed manifolds which may not be orientable
Naoki Kitazawa
The Reeb space of a smooth function is a topological and combinatoric object and fundamental and important in understanding topological and geometric properties of the manifold of…
Smooth functions with simple structures on 3-dimensional closed manifolds with prescribed Reeb graphs and preimages
Naoki Kitazawa
We give a new answer to so-called realization problems of graphs as Reeb graphs of smooth functions with prescribed preimages of regular values having nice structures. We present a…
Realization problems of graphs as Reeb graphs of Morse functions with prescribed preimages
Naoki Kitazawa
The present paper is on a new result on so-called realization problems of graphs as Reeb graphs of Morse functions with prescribed preimages. The Reeb graph of a smooth function is…
Characterizing families of graph manifolds via suitable classes of simple fold maps into the plane and embeddability of the Reeb spaces in some 3-dimensional manifolds
Naoki Kitazawa
Graph manifolds form important classes of -dimensional closed and orientable manifolds. For example, {\it Seifert} manifolds are graph manifolds where hyperbolic manifolds are n…
On simple classes of special generic maps and round fold maps and fold maps obtained by composing projections
Naoki Kitazawa
Fold maps are fundamental tools in the theory of singularities of differentiable maps and its applications to geometry. They are higher dimensional variants of Morse functions. Cla…