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Caustics and wave front propagations: applications to differential geometry

Shyuichi Izumiya, Masatomo Takahashi (2008)

Banach Center Publications

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.

Caustique mystique

Daniel Bennequin (1984/1985)

Séminaire Bourbaki

Caustiques et catastrophes

J. Petitot (1978)

Mathématiques et Sciences Humaines

Characterizations of $H_{x} 1$ -sufficiency of jets

Le Tien Tam (1986)

Annales Polonici Mathematici

Classification C...des équations de pfaff complètement intégrables à singularité isolée.

R. Moussu (1983)

Inventiones mathematicae

Classification of $𝒜$ -simple germs from $k^{n}$ to $k^{2}$

J. H. Rieger, M. A. S. Ruas (1991)

Compositio Mathematica

Classification of singularities with compact abelian symmetry

Gordon Wassermann (1988)

Banach Center Publications

Classifying Spaces of b-Stable Whitney Coverings.

Ute Twisselmann (1990)

Forum mathematicum

Coisotropic varieties and their generating families

S. Janeczko (1992)

Annales de l'I.H.P. Physique théorique

Combinatorial structure of Stokes regions of a simple singularity.

Jianming Yu (1996)

Mathematische Annalen

Conformally invariant variational integrals and the removability of isolated singularities.

Michael Grüter (1984)

Manuscripta mathematica

Constructing generic smooth maps of a manifold into a surface with prescribed singular loci

Osamu Saeki (1995)

Annales de l'institut Fourier

It is known that the singular set $S (f)$ of a generic smooth map $f : M \to N$ of an $n$ -dimensional manifold into a surface is a closed 1-dimensional submanifold of $M$ and that it has a natural stratification induced by the absolute index. In this paper, we give a complete characterization of those 1-dimensional (stratified) submanifolds which arise as the singular set of a generic map in terms of the homology class they represent.

Cycles and measure of bifurcation sets for two-dimensional diffeomorphisms.

J., Takens, F. Palis (1985)

Inventiones mathematicae

Displaying 1 – 13 of 13

Currently displaying 1 – 13 of 13