100
V. Hussin et al.
Acknowledgments ˙
IY thanks the Centre de Recherches Mathématiques, Université de Montréal,
where part of this work was done, for the kind hospitality. VH acknowledges the support of research
grants from NSERC of Canada. Several discussions with W J Zakrzewski have been very fruitful.
References
1. D.G. Gross, T. Piran, S. Weinberg, Two Dimensional Quantum Gravity and Random Surfaces
(World Scientific, Singapore, 1992)
2. S. Safram, Statistical Thermodynamics of Surfaces Interface and Membranes (AddisonWesley, Massachusetts, 1994)
3. R. Rajaraman, CP N solitons in quantum Hall systems. Eur. Phys. B 28, 157–162 (2002)
4. N. Manton, P. Sutcliffe, Topological Solitons (Cambridge University Press, New York, 2004)
5. W.J. Zakrzewski, Low Dimensional Sigma Models (Adam Hilger, Bristol, 1989)
6. E. Witten, Supersymmetric form of the nonlinear σ model in two dimensions. Phys. Rev. D 16,
2991–2994 (1977)
7. L. Delisle, V. Hussin, W.J. Zakrzewski, Constant curvature solutions of Grassmannian sigma
models: (1) Holomorphic solutions. J. Geom. Phys. 66, 24–36 (2013)
8. L. Delisle, V. Hussin, W.J. Zakrzewski, Constant curvature solutions of Grassmannian sigma
models: (2) Non-holomorphic solutions. J. Geom. Phys 71, 1–10 (2013)
9. Z.Q. Li, Z.H. Yu, Constant curved minimal 2-spheres in G(2, 4). Manuscripta Math. 100,
305–316 (1999)
10. X.X. Jiao, J.G. Peng, Classification of holomorphic spheres of constant curvature in complex
Grassmann manifold G(2, 5). Diff. Geom. Appl. 20, 267–277 (2004)
11. L. Delisle, V. Hussin, ˙
I. Yurdu¸ sen, W.J. Zakrzewski, Constant curvature surfaces of the
supersymmetric CP N −1 sigma model. J. Math. Phys. 56, 023506-1–023506-18 (2015)
12. L. Delisle, V. Hussin, W.J. Zakrzewski, General construction of solutions of the supersymmetric CP N −1 sigma model. J. Math. Phys 57, 023506 (2016)
13. V. Hussin, M. Lafrance, ˙
I. Yurdu¸ sen, W.J. Zakrzewski, Holomorphic solutions of the susy
Grassmannian σ -model and gauge invariance. J. Phys. A Math. Theor. 51, 185401-1–1854018 (2018)
14. A.J. MacFarlane, Generalizations of σ -models and CP N models and instantons. Phys. Lett. B
82, 239–241 (1978)
V. Hussin et al.
Acknowledgments ˙
IY thanks the Centre de Recherches Mathématiques, Université de Montréal,
where part of this work was done, for the kind hospitality. VH acknowledges the support of research
grants from NSERC of Canada. Several discussions with W J Zakrzewski have been very fruitful.
References
1. D.G. Gross, T. Piran, S. Weinberg, Two Dimensional Quantum Gravity and Random Surfaces
(World Scientific, Singapore, 1992)
2. S. Safram, Statistical Thermodynamics of Surfaces Interface and Membranes (AddisonWesley, Massachusetts, 1994)
3. R. Rajaraman, CP N solitons in quantum Hall systems. Eur. Phys. B 28, 157–162 (2002)
4. N. Manton, P. Sutcliffe, Topological Solitons (Cambridge University Press, New York, 2004)
5. W.J. Zakrzewski, Low Dimensional Sigma Models (Adam Hilger, Bristol, 1989)
6. E. Witten, Supersymmetric form of the nonlinear σ model in two dimensions. Phys. Rev. D 16,
2991–2994 (1977)
7. L. Delisle, V. Hussin, W.J. Zakrzewski, Constant curvature solutions of Grassmannian sigma
models: (1) Holomorphic solutions. J. Geom. Phys. 66, 24–36 (2013)
8. L. Delisle, V. Hussin, W.J. Zakrzewski, Constant curvature solutions of Grassmannian sigma
models: (2) Non-holomorphic solutions. J. Geom. Phys 71, 1–10 (2013)
9. Z.Q. Li, Z.H. Yu, Constant curved minimal 2-spheres in G(2, 4). Manuscripta Math. 100,
305–316 (1999)
10. X.X. Jiao, J.G. Peng, Classification of holomorphic spheres of constant curvature in complex
Grassmann manifold G(2, 5). Diff. Geom. Appl. 20, 267–277 (2004)
11. L. Delisle, V. Hussin, ˙
I. Yurdu¸ sen, W.J. Zakrzewski, Constant curvature surfaces of the
supersymmetric CP N −1 sigma model. J. Math. Phys. 56, 023506-1–023506-18 (2015)
12. L. Delisle, V. Hussin, W.J. Zakrzewski, General construction of solutions of the supersymmetric CP N −1 sigma model. J. Math. Phys 57, 023506 (2016)
13. V. Hussin, M. Lafrance, ˙
I. Yurdu¸ sen, W.J. Zakrzewski, Holomorphic solutions of the susy
Grassmannian σ -model and gauge invariance. J. Phys. A Math. Theor. 51, 185401-1–1854018 (2018)
14. A.J. MacFarlane, Generalizations of σ -models and CP N models and instantons. Phys. Lett. B
82, 239–241 (1978)