24 citations · 171 across the 71 of their papers we have counts for
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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…
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…
Some remark on real algebraic maps which are topologically special generic maps and generalize the canonical projections of the unit spheres
Naoki Kitazawa
Morse functions with exactly two singular points on homotopy spheres and canonical projections of spheres are generalized as special generic maps. A special generic map is, roughly…
Notes on Reeb graphs of real algebraic functions which may not be planar
Naoki Kitazawa
The Reeb graph of a smooth function is a graph being a natural quotient space of the manifold of the domain and the space of all connected components of preimages. Such a combinato…
Explicit smooth real algebraic functions which may have both compact and non-compact preimages on smooth real algebraic manifolds
Naoki Kitazawa
In our previous work, we have constructed explicit smooth real algebraic functions which may have both compact and non-compact preimages on smooth real algebraic manifolds. This pa…
On real algebraic maps whose images are domains surrounded by the products of hyperbolas and real affine spaces
Naoki Kitazawa
Previously, we have systematically constructed explicit real algebraic functions which are represented as the compositions of smooth real algebraic maps whose images are domains su…
Explicit real algebraic functions which may have both compact and non-compact preimages
Naoki Kitazawa
As a pioneering work we construct explicit real algebraic functions which may have both compact and non-compact preimages. The author has obtained explicit real algebraic functions…
Reconstructing real algebraic maps locally like moment-maps with prescribed images and compositions with the canonical projections to the -dimensional real affine space
Naoki Kitazawa
We present new real algebraic maps of non-positive codimensions with prescribed images whose boundaries consist of explicit non-singular real algebraic hypersurfaces satisfying so-…
Construction of real algebraic functions with prescribed preimages
Naoki Kitazawa
Nash and Tognoli show that smooth closed manifolds can be the zero sets of some real polynomial maps and non-singular. The canonical projections of spheres naturally embedded in th…