1 |
J. Guven, D.M. Valencia and J. Vazquez-Montejo, Environmental bias and elastic curves on surfaces, Phys. A: Math Theory. 47 (2014), 355201.
DOI
|
2 |
G. Kirchhoff, Uber Das Gleichgewicht und die Bewegung einer elastichen Scheibe, Crelles J. 40 (1850), 51-88.
|
3 |
B. Kolev, Lie groups and mechanics: an introduction, J. Nonlinear Math. Phys. 11 (2004), 480-498.
DOI
|
4 |
T. Korpinar, New Characterization for Minimizing Energy of Biharmonic Particles in Heisenberg Spacetime, Int J Phys. 53 (2014), 3208-3218.
DOI
|
5 |
T. Lopez-Leon, V. Koning, K..S. Devaiah, V. Vitelli and A.A. Fernandez-Nieves, Frustrated nematic order in spherical geometries, Nature Phys. 7 (2011), 391-394.
DOI
|
6 |
T. Lopez-Leon, A.A. Fernandez-Nieves, M. Nobili and C. Blanc, Nematic-Smectic Transition in Spherical Shells, Phys. Rev. Lett. 106 (2011), 247802.
DOI
|
7 |
A.E.H. Love, A Treatise on the Mathematical Theory of Elasticity, 2013.
|
8 |
J. Milnor, Curvatures of Left-Invariant Metrics on Lie Groups, Advances in Mathematics. 21 (1976), 293-329.
DOI
|
9 |
D. Mumfordg, Elastica and Computer Vision, Algebraic Geometry and its Applications, Springer-Verlag, New-York, 1994.
|
10 |
T. Schoenemann, F. Kahl, S. Masnou and D. Cremers, A linear framework for region-based image segmentation and inpainting involving curvature penalization, International Journal of Computer Vision. 99 (2012), 53-68.
DOI
|
11 |
D.A. Singer, Lectures on Elastic Curves and Rods, 2007.
|
12 |
E. Catmull and J. Clark, Recursively generated b-spline surfaces on arbitrary topological surfaces, Computer-Aided Design. 10 (1978), 350-355.
DOI
|
13 |
D. Terzopoulost, J. Platt, A. Barr and K. Fleischert, Elastically Deformable Models, Computer Graphics. 21 (1987), 205-214.
DOI
|
14 |
C.M. Wood, On the Energy of a Unit Vector Field, Geom. Dedic. 64 (1997), 319-330.
DOI
|
15 |
J.S. Milne, Algebraic Groups, Lie Groups, and their Arithmetic Subgroups, 2011.
|
16 |
G. Altay and H. Oztekin, Translation surfaces Generated by Manheim Curves in Three Dimensional Euclidean Space, Gen. Math Notes. 26 (2015), 28-34.
|
17 |
A. Altin, On the energy and Pseduoangle of Frenet Vector Fields in , Ukrainian Math. Journal. 63 (2011), 969-976.
DOI
|
18 |
V.I. Arnold, Sur la g'eom'etrie diff'erentielle des groupes de Lie de dimension infinie et ses applications 'a l'hydrodynamique des uides parfaits, Ann. Inst. Fourier Grenoble. 16 (1966), 319-361.
|
19 |
E. Bretin, J.O. Lachaud and E. Oudet, Regularization of discrete contour by Willmore energy, Journal of Mathematical Imaging and Vision. 40 (2011), 214-229.
DOI
|
20 |
P.M. Chacon and A.M. Naveira, Corrected Energy of Distrubution on Riemannian Manifolds, Osaka J. Math. 41 (2004), 97-105.
|
21 |
P. Crouch and L.F. Silva, The dynamic interpolation problem: on Riemannian manifolds, Lie groups, and symmetric spaces, J. Dynam. Control Systems. 1 (1995), 177-202.
DOI
|
22 |
P.M. Chacon, A.M. Naveira and J.M. Weston, On the Energy of Distributions, with Application to the Quaternionic Hopf Fibrations, Monatsh. Math. 133 (2001), 281-294.
DOI
|
23 |
U. Ciftci, A generalization of Lancert's theorem, J. Geom. Phys. 59 (2009), 1597-1603.
DOI
|
24 |
G. Citti and A. Sarti, Cortical Based Model of Perceptual Completion in the Roto-Translation Space, Journal of Mathematical Imaging and Vision. 24 (2006), 307-326.
DOI
|
25 |
O. Gil Medrano, Relationship between volume and energy of vector fields, Differential Geometry and its Applications. 15 (2001), 137-152.
DOI
|