Signature submanifolds for some equivalence problems

Journal of Linear and Topological Algebra

مقاله 1، دوره 03، شماره 03، آذر 2014، صفحه 121-130   

نویسندگان

M. Nadjakhah^* ؛ Z. Pahlevani Tehrani

Iran University of Science and Technology, Tehran, Iran

چکیده

This article concerned on the study of signature submanifolds for curves under Lie group actions SE(2), SA(2) and for surfaces under SE(3). Signature submanifold is a regular submanifold which its coordinate components are differential invariants of an associated manifold under Lie group action, and therefore signature submanifold is a key for solving equivalence problems.

کلیدواژه‌ها

Signature submanifold؛ equivalence problem؛ moving frame؛ differential invariant

مراجع

[1] M. Fels and P. J. Olver, Moving coframes. II. Regularization and theoretical foundations, Acta Appl. Math.55 (1999), 127-208.

 

[2] P. J. Olver, Equivalence, invariant and symmetry, Cambridge University Press, Cambridge (1995).

 

[3] P. J. Olver, Applications of Lie groups to differential equations, Springer Verlag, Second Edition, GTM, Vol. 107, New York, (1993).

 

[4] P. J. Olver, Differential Invariant Algebra, Comtemp. Math. 549 (2011), 95-121.

 

[5] P. J. Olver, Lectures on Moving frames, London Math. Soc. Lecture Note Series, vol. 381 Cambridge University Press Cambridge, 2011, pp.207-246.

 

[6] E. L. Mansfeld, A Practical Guide to the Invariant Calculus, Cambridge University Press, Cambridge 2010.