Invariants of curves in \(\mathbb RP^2\) and \(\mathbb R^2\). (English) Zbl 1128.53010

Thompson, Abigail

Algebr. Geom. Topol. 6, 2175-2186 (2006).

Summary: There is an elegant relation [cf. Fr. Fabricius-Bjerre, Math. Scand. 40, 20–24 (1977; Zbl 0352.50011)] among the double tangent lines, crossings, inflections points, and cusps of a singular curve in the plane. We give a new generalization to singular curves in \(\mathbb RP^2\). We note that the quantities in the formula are naturally dual to each other in \(\mathbb RP^2\), and we give a new dual formula.

MSC:

53A20	Projective differential geometry
53A04	Curves in Euclidean and related spaces
14H50	Plane and space curves

Keywords:

knots; \(\mathbb RP^2\); plane curves; singular curves

Citations:

Zbl 0352.50011

References:

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