A Global View on Generic Geometry

  • María del Carmen Romero FusterEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 222)


We describe how the study of the singularities of height and distance squared functions on submanifolds of Euclidean space, combined with adequate topological and geometrical tools, shows to be useful to obtain global geometrical properties. We illustrate this with several results concerning closed curves and surfaces immersed in \(\mathbb {R}^n\) for \(n=3,4, 5\).


Stratifications Height functions Distance squared functions Curvature locus Vertices Semiumbilics Inflection points Convexity 2-regular immersions. 

MS classification

58K05 58C27 53C42 57R30 


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Authors and Affiliations

  1. 1.Departament de MatemàtiquesUniversitat de ValènciaBurjassot (València)Spain

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