Frontal Singularities and Related Problems

Goo Ishikawa ()
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Goo Ishikawa: Hokkaido University, Department of Mathematics, Faculty of Sciences

Chapter Chapter 4 in Handbook of Geometry and Topology of Singularities VII, 2025, pp 203-271 from Springer

Abstract: 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.

Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-68711-2_4

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DOI: 10.1007/978-3-031-68711-2_4

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