Artículos de revistas
A Weierstrass Representation Formula For Minimal Surfaces In ℍ3 And ℍ2 × ℝ
Registro en:
Acta Mathematica Sinica, English Series. , v. 22, n. 6, p. 1603 - 1612, 2006.
14398516
10.1007/s10114-005-0637-y
2-s2.0-33749618336
Autor
Mercuri F.
Montaldo S.
Piu P.
Institución
Resumen
We give a general setting for constructing a Weierstrass representation formula for simply connected minimal surfaces in a Riemannian manifold. Then, we construct examples of minimal surfaces in the three dimensional Heisenberg group and in the product of the hyperbolic plane with the real line. © 2006 Springer-Verlag. 22 6 1603 1612 Barbosa, J.L.M., Colares, A.G., Minimal surfaces in ℝ3 (1986) Lecture Notes in Mathematics, p. 1195. , Springer-Verlag, Berlin Gray, A., (1998) Modern Differential Geometry of Curves and Surfaces with Mathematica, Second Edition, , CRC Press, Boca Raton, FL Bekkar, M., Exemples de surfaces minimales dans l'espace de Heisenberg (1991) Rend. Sem. Fac. Sci. Univ. Cagliari, 61, pp. 123-130 Bekkar, M., Sari, T., Surfaces minimales réglées dans l'espace de Heisenberg H3 (1992) Rend. Sem. Mat. Univ. Politec. Torino, 50, pp. 243-254 Caddeo, R., Piu, P., Ratto, A., SO(2)-invariant minimal and constant mean curvature surfaces in 3-dimensional homogeneous spaces (1995) Manuscripta Math., 87, pp. 1-12 Figueroa, C.B., Mercuri, F., Pedrosa, R.H.L., Invariant surfaces of the Heisenberg groups (1999) Ann. Mat. Pura Appl., 177 (4), pp. 173-194 Piu, P., Sanini, A., One-parameter subgroups and minimal surfaces in the Heisenberg group (1998) Note Mat., 18, pp. 143-153 Scott, D.P., Minimal Surfaces in the Heisenberg Group, , preprint Nelli, B., Rosenberg, H., Minimal surfaces in ℍ2 x ℍ (2002) Bull. Braz. Math. Soc. (N.S.), 33, pp. 263-292 Kokubu, M., Weierstrass representation for minimal surfaces in hyperbolic space (1997) Tohoku Math. J., 49, pp. 367-377 Koszul, J.L., Malgrange, B., Sur certaines fibrées complexes (1958) Arch. Math., 9, pp. 102-109 Eells, J., Sampson, J.H., Harmonic mappings of Riemannian manifolds (1964) Amer. J. Math., 86, pp. 109-160 Eells, J., Lemaire, L., Selected topics in harmonic maps (1983) AMS Regional Conference Series in Mathematics, p. 50 Inoguchi, J., Kumamoto, T., Ohsugi, N., Suyama, Y., Differential geometry of curves and surfaces in 3-dimensional homogeneous spaces I and II (1999) Fukuoka Univ. Sci. Rep., 29-30 Figueroa, C.B., Geometria Das Subvariedades Do Grupo de Heisenberg, , Ph.d Thesis, Campinas Rosenberg, H., Minimal surfaces in double-struck M2 x ℝ (2002) Illinois J. Math., 46, pp. 1177-1195