7 papers
Fundamental examples of height functions on closed manifolds and their 1st derivatives
Naoki Kitazawa
Height functions are fundamental and important in mathematics, especially in geometry, more explicitly, singularity theory of differentiable maps and applications to differential t…
Regions represented as foliated forms and natural smooth maps onto them
Naoki Kitazawa
The author is interested in regions surrounded by hypersurfaces and natural smooth maps onto them respecting the canonical projections of the unit spheres and so-called special gen…
Fundamental examples of Reeb spaces of smooth functions defined from two graphs of smooth functions with same asymptotic behaviors
Naoki Kitazawa
Reeb spaces of (continuous) real-valued functions on (nice) topological spaces are the spaces whose underlying sets consist of all connected components (contours) of their level se…
A note on Reeb spaces of some explicit real analytic functions
Naoki Kitazawa
Reeb spaces of smooth functions are fundamental and strong tools in understanding manifolds via smooth functions with mild critical points. They are defined as the natural spaces o…
On real algebraic realization of round fold maps of codimension
Naoki Kitazawa
The canonical projections of the unit spheres are generalized to special generic maps and round fold maps, for example. They are generalizations from the viewpoint of singularity t…
Smooth functions which are Morse on preimages of values not being local extrema and constructing natural functions of the class on connected sums of manifolds admitting these functions
Naoki Kitazawa
We discuss smooth functions which are Morse on preimages of values not being local extrema. We call such a function internally Morse or I-Morse. The Reeb graph of a smooth function…