Journal for Geometry and Graphics 7 (2003), No. 2, 145--156
Copyright Heldermann Verlag 2003
Shapes of Space Curves
Faculty of Mathematics and Informatics, Shumen University, Alen Mak Str. 115, Shumen 9712, Bulgaria, firstname.lastname@example.org
Faculty of Mathematics and Informatics, Shumen University, Alen Mak Str. 115, Shumen 9712, Bulgaria, email@example.com
We study an ordered pair of functions which determines a regular space curve up to a direct similarity. The first function is called a shape curvature and the second one a shape torsion. We prove an extension of the fundamental theorem of space curves relating to the group of direct similarities. We also propose a direct way for recovering a space curve from its shape curvature and shape torsion.
Keywords: space curves, direct similarities, differential-geometric invariants.
MSC: 53A55; 53A04.
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