On generic hypersurfaces in ℝⁿ

J.W. Bruce

doi:10.1017/S0305004100058862

On generic hypersurfaces in ℝⁿ

J.W. Bruce

Research output: Contribution to journal › Article (journal) › peer-review

Abstract

In this paper we consider certain questions concerning the differential geometry of generic hypersurfaces in n. Our results prove, for example, that the curve of rib points of a generic surface in 3 has transverse self-intersections. In (4) Porteous discussed (amongst other things) the generic geometry of curves and surfaces in 3. Subsequently Looijenga ((3) and see also (5)) gave a more precise definition of the term generic and showed that an open dense subset of smooth embeddings of manifolds in Euclidean space were indeed generic.

Original language	English
Pages (from-to)	389-394
Journal	Mathematical Proceedings of the Cambridge Philosophical Society
Volume	90
Issue number	3
DOIs	https://doi.org/10.1017/S0305004100058862
Publication status	Published - 1981

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title = "On generic hypersurfaces in ℝⁿ",

abstract = "In this paper we consider certain questions concerning the differential geometry of generic hypersurfaces in n. Our results prove, for example, that the curve of rib points of a generic surface in 3 has transverse self-intersections. In (4) Porteous discussed (amongst other things) the generic geometry of curves and surfaces in 3. Subsequently Looijenga ((3) and see also (5)) gave a more precise definition of the term generic and showed that an open dense subset of smooth embeddings of manifolds in Euclidean space were indeed generic.",

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AB - In this paper we consider certain questions concerning the differential geometry of generic hypersurfaces in n. Our results prove, for example, that the curve of rib points of a generic surface in 3 has transverse self-intersections. In (4) Porteous discussed (amongst other things) the generic geometry of curves and surfaces in 3. Subsequently Looijenga ((3) and see also (5)) gave a more precise definition of the term generic and showed that an open dense subset of smooth embeddings of manifolds in Euclidean space were indeed generic.

U2 - 10.1017/S0305004100058862

DO - 10.1017/S0305004100058862

M3 - Article (journal)

SN - 0305-0041

VL - 90

SP - 389

EP - 394

JO - Mathematical Proceedings of the Cambridge Philosophical Society

JF - Mathematical Proceedings of the Cambridge Philosophical Society

IS - 3

ER -

On generic hypersurfaces in ℝⁿ

Abstract

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