Signature submanifolds for some equivalence problems

الموضوعات :

M. Nadjakhah ¹ (Iran University of Science and Technology, Tehran, Iran)
Z. Pahlevani Tehrani ² (Iran University of Science and Technology, Tehran, Iran)

تاريخ الإرسال : 25 السبت , ذو القعدة, 1435 تاريخ التأكيد : 23 الإثنين , صفر, 1436 تاريخ الإصدار : 28 السبت , صفر, 1436

الکلمات المفتاحية: Signature submanifold, moving frame, equivalence problem, differential invariant,

ملخص المقالة :

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

المصادر:

[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.