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Frontal Singularities and Related Problems

In: Handbook of Geometry and Topology of Singularities VII

Author

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  • Goo Ishikawa

    (Hokkaido University, Department of Mathematics, Faculty of Sciences)

Abstract

This is a survey of C ∞ $$C^\infty $$ or complex analytic frontal singularities. A mapping from a manifold of dimension n to a manifold of dimension m with n ≤ m $$n \leq m$$ is called a frontal, if its differential is well-controlled by a field of tangential n-planes on the target manifold along the mapping which contain images by the differentials of tangent spaces to the source manifold. We explain the basic theory on frontal hypersurfaces, the case m = n + 1 $$m = n+1$$ , and then their generalisations in real and complex cases. We mention several notions, topics and problems which are related to frontal singularities from rather wide aspects with future expects.

Suggested Citation

  • Goo Ishikawa, 2025. "Frontal Singularities and Related Problems," Springer Books, in: José Luis Cisneros-Molina & Lê Dũng Tráng & José Seade (ed.), Handbook of Geometry and Topology of Singularities VII, chapter 0, pages 203-271, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-68711-2_4
    DOI: 10.1007/978-3-031-68711-2_4
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