The Gauss map of hypersurfaces in 2-step nilpotent lie groups
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 2 (2006) no. 2, pp. 186-206 Cet article a éte moissonné depuis la source Math-Net.Ru

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Ye. V. Petrov. The Gauss map of hypersurfaces in 2-step nilpotent lie groups. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 2 (2006) no. 2, pp. 186-206. http://geodesic.mathdoc.fr/item/JMAG_2006_2_2_a5/

[1] J. L. Barbosa, M. P. do Carmo, J. Eschenburg, “Stability of Hypersurfaces with Constant Mean Curvature in Riemannian Manifolds”, Math. J., 197 (1988), 123–138 | DOI | MR | Zbl

[2] T. H. Colding, W. P. Minikozzi, II, Minimal Surfaces, Courant Inst. Math. Sci., 4, New York Univ., New York, 1999 | MR | Zbl

[3] P. B. Eberlein, “Geometry of 2-Step Nilpotent Groups with a Left-Invariant Metric”, Ann. Sci. École Norm. Sup., 27 (1994), 611–660 | MR | Zbl

[4] P. B. Eberlein, “Geometry of 2-Step Nilpotent Groups with a Left-Invariant Metric, II”, Trans. Amer. Math. Soc., 343 (1994), 805–828 | DOI | MR | Zbl

[5] P. B. Eberlein, “The Moduli Space of 2-Step Nilpotent Lie Algebras of Type $(p,q)$”, Contemp. Math., 332 (2003), 37–72 | DOI | MR | Zbl

[6] N. do Espirito-Santo, S. Fornari, K. Frensel, J. Ripoll, “Constant Mean Curvature Hypersurfaces in a Lie Group with a Bi-Invariant Metric”, Manuscripta Math., 111 (2003), 459–470 | DOI | MR | Zbl

[7] D. Fischer-Colbrie, R. Schoen, “The Structure of Complete Stable Minimal Surface in 3-Manifolds of Nonnegative Scalar Curvature”, Comm. Pure Appl. Math., 33 (1980), 199–211 | DOI | MR | Zbl

[8] G. B. Folland, Harmonic Analysis in Phase Space, Ann. Math. Stud., 122, Princeton Univ. Press, Princeton, 1989 | MR | Zbl

[9] L. A. Masal'tsev, “A Version of the Ruh-Vilms Theorem for Surfaces of Constant Mean Curvature in $S^3$”, Math. Notes, 73 (2003), 85–96 | DOI | MR | Zbl

[10] L. A. Masal'tsev, “Harmonic Properties of Gauss Mappings in $H^3$”, Ukr. Math. J., 55 (2003), 588–600 | DOI | MR | Zbl

[11] J. Milnor, “Curvatures of Left Invariant Metrics on Lie Groups”, Adv. Math., 21 (1976), 293–329 | DOI | MR | Zbl

[12] E. A. Ruh, J. Vilms, “The Tension Field of the Gauss Map”, Trans. Amer. Math. Soc., 149 (1970), 569–573 | DOI | MR | Zbl

[13] A. Sanini, “Gauss Map of a Surface of the Heisenberg Group”, Boll. Unione Mat. It., 11-B(7):suppl. fasc. 2 (1997), 79–93 | MR | Zbl

[14] H. Urakawa, Calculus of Variations and Harmonic Maps, Transl. Math. Monogr., 132, AMS, Providence, RI, 1993 | MR | Zbl