Lancret's Theorem

The set of Lancret is a result from differential geometry . It was formulated by Michel-Ange Lancret (1774–1807) in 1802. The first complete evidence comes from Barré de Saint-Venant .

statement

A three times continuously differentiable curve with nowhere vanishing curvature is exactly then a slope line , if its torsion is a constant multiple of its curvature . A curve is called an embankment line, or a generalized helix, if its tangents always form the same angle with a fixed direction. An example of a slope line is the helix .

Individual evidence

↑ Erwin Kreyszig: Differential Geometry (= Mathematical Expositions 11, ISSN 0076-5333 ). University of Toronto Press, Toronto, 1959, Thm. 15.1, p. 41 (Reprinted: Dover Publications, New York, 1991, ISBN 0-486-66721-9 ).
↑ Dirk J. Struik: Lectures on Classical Differential Geometry . Second edition, Addison-Wesley, Reading, 1961, par. 1-9, p. 34 (Reprinted by Dover Publications, New York, 1988, ISBN 0-486-65609-8 ).

[1] Erwin Kreyszig: Differential Geometry (= Mathematical Expositions 11, ISSN 0076-5333 ). University of Toronto Press, Toronto, 1959, Thm. 15.1, p. 41 (Reprinted: Dover Publications, New York, 1991, ISBN 0-486-66721-9 ).

[2] Dirk J. Struik: Lectures on Classical Differential Geometry . Second edition, Addison-Wesley, Reading, 1961, par. 1-9, p. 34 (Reprinted by Dover Publications, New York, 1988, ISBN 0-486-65609-8 ).