Differentiable curves of cyclic order four

Spoar, G.

doi:10.2140/pjm.1982.102.209

Pacific J. Math.

1982

DOI: 10.2140/pjm.1982.102.209

|View full text |Cite

Differentiable curves of cyclic order four

G. Spoar¹

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

1987

1996

Publication Types

Select...

Article4

Relationship

Self Cite1

Independent3

Authors

Journals

Cited by 4 publications

(1 citation statement)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In some of these cases there are analogues of the Four-vertex Theorem; i.e., results on the minimum number of Of'-singular points of a JU-differentiable curve of Jd-order > k. Also the classification of the Jd-differentiable curves of~-order (k + 1) is known in some cases [2], [16]. In both of these topics more research seems desirable.…”

mentioning

confidence: 99%

Independence structures in the geometry of orders

Lane

Scherk²,

Turgeon

1987

Aeq. Math.

View full text Add to dashboard Cite

Dedicated to Professor Otto Haupt with best wishes on his lOOth birthday1. An Arc [A curve] is the homeomorphic image of a segment [of the projective line].The geometry of orders of arcs and curves is developed in [2]. In a fundamental domain G, a set #g of curves and arcs K is given. The geometry of orders studies the structure of a given arc B, the basic arc, by means of the set #g. This set #g of characteristic curves has a dimension, the fundamental number k = k(#g). In the local theory, a point p on B, the base point, is introduced, and the behaviour of B near p is examined. For details we refer to the first pages of [2]. However, the following concepts are central: The #g-order of B is the number sup ] K n B I. The #g-order ofp is the #g-order Ke~" of a sufficiently small neighbourhood of p on B. The point p is #g-singular if this number is greater than k.2. Within the framework of the geometry of orders, various mathematicians have done direct differential geometry. Choosing some #g, they defined differentiability with respect to #g and classified the #g-differentiable points. Then they proved theorems on their #g-order. Their sets #g and fundamental domains G were

show abstract

mentioning

confidence: 99%

Independence structures in the geometry of orders

Lane

Scherk²,

Turgeon

1987

Aeq. Math.

View full text Add to dashboard Cite

show abstract

Normal arcs and curves of K-order k+1

Spoar

1996

Geom Dedicata

View full text Add to dashboard Cite

show abstract

A generalized four-vertex theorem

Spoar

1988

J Geom

View full text Add to dashboard Cite

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

hi@scite.ai

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Differentiable curves of cyclic order four

Cited by 4 publications

References 7 publications

Independence structures in the geometry of orders

Independence structures in the geometry of orders

Normal arcs and curves of K-order k+1

A generalized four-vertex theorem

Contact Info

Product

Resources

About