About the Bonnet System of Invariants of a Surface in the Euclidean Space
Abstract
Let be the set of all coefficients of the first and second fundamental forms of a surface in a Euclidean space. Using computations of invariants from K for some surfaces, it is proved that K is a minimal complete system of SM(3) -invariants of a regular surface in, where SM(3) is the group of all special Euclidean motions of.
Keywords
Kaynakça
- Gray, A.,1998. Modern Differential Geometry of Curves and Surfaces with Mathematica,CRC press.
- Kaya, Y., Küçük, A. ve Melekoğlu, A.,2015, Diferensiyel Geometriye Giriş,(çev:Yusuf Kaya(eds)), Dora yayınları, ISBN 978-605-9929-34-9,Bursa.
- Khadjiev, D.,2010. Complete systems of differential invariants of vector fields in a Euclidean space, Turk. J. Math,34,543-559.
- Khadjiev D., Ören İ. and Pekşen Ö.,2013. Generating systems of differential invariants and the theorem on existence for curves in the pseudo-Euclidean geometry. Turk J Math, 37(1), 80-94.
- Kose, Z., Toda, M., and Aulisa, E.,2011. Solving Bonnet problems to construct families of surfaces, Balkan J. Geom.Appl.,16(2),70-80.
- Ören İ.,2016. Equivalence conditions of two Bézier curves in the Euclidean geometry,
- Sibirskii, K. S.,1976. Algebraic Invariants of Differential Equations and Matrices, Kishinev, Stiintsa.