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1
Content available remote

Systems of Clairaut type

100%
Izumiya S.
Colloquium Mathematicum
|
1993
|
tom 66
|
nr 2
219-226
EN
A characterization of systems of first order differential equations with (classical) complete solutions is given. Systems with (classical) complete solutions that consist of hyperplanes are also characterized.
2
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Formation of singularities for viscosity solutions of Hamilton-Jacobi equations

64%
Izumiya S., Kossioris G. T.
Banach Center Publications
|
1996
|
tom 33
|
nr 1
127-148
3
Content available remote

Caustics and wave front propagations: applications to differential geometry

64%
Izumiya S., Takahashi M.
Banach Center Publications
|
2008
|
tom 82
|
nr 1
125-142
EN
This is mainly a survey on the theory of caustics and wave front propagations with applications to differential geometry of hypersurfaces in Euclidean space. We give a brief review of the general theory of caustics and wave front propagations, which are well-known now. We also consider a relationship between caustics and wave front propagations which might be new. Moreover, we apply this theory to differential geometry of hypersurfaces, getting new geometric properties.
4
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Curves and surfaces in hyperbolic space

51%
Izumiya S., Pei D., Takahashi M.
Banach Center Publications
|
2004
|
tom 65
|
nr 1
107-123
EN
In the first part (Sections 2 and 3), we give a survey of the recent results on application of singularity theory for curves and surfaces in hyperbolic space. After that we define the hyperbolic canal surface of a hyperbolic space curve and apply the results of the first part to get some geometric relations between the hyperbolic canal surface and the centre curve.
5
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The rectifying developable and the spherical Darboux image of a space curve

51%
Izumiya S., Katsumi H., Yamasaki T.
Banach Center Publications
|
1999
|
tom 50
|
nr 1
137-149
EN
In this paper we study singularities of certain surfaces and curves associated with the family of rectifying planes along space curves. We establish the relationships between singularities of these subjects and geometric invariants of curves which are deeply related to the order of contact with helices.
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