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

2 Citations (Scopus)

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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PY - 1981

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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

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