## Duke Mathematical Journal

### Complex tangents of real surfaces in complex surfaces

Franc Forstnerič

#### Article information

Source
Duke Math. J. Volume 67, Number 2 (1992), 353-376.

Dates
First available in Project Euclid: 20 February 2004

https://projecteuclid.org/euclid.dmj/1077294407

Digital Object Identifier
doi:10.1215/S0012-7094-92-06713-5

Mathematical Reviews number (MathSciNet)
MR1177310

Zentralblatt MATH identifier
0761.53032

#### Citation

Forstnerič, Franc. Complex tangents of real surfaces in complex surfaces. Duke Math. J. 67 (1992), no. 2, 353--376. doi:10.1215/S0012-7094-92-06713-5. https://projecteuclid.org/euclid.dmj/1077294407.

#### References

• [1] R. Abraham, Transversality in manifolds of mappings, Bull. Amer. Math. Soc. 69 (1963), 470–474.
• [2] R. Abraham and J. Robbin, Transversal mappings and flows, An appendix by Al Kelley, W. A. Benjamin, Inc., New York-Amsterdam, 1967.
• [3] L. V. Ahlfors and L. Sario, Riemann surfaces, Princeton Mathematical Series, No. 26, Princeton University Press, Princeton, N.J., 1960.
• [4] A. Andreotti and T. Frankel, The Lefschetz theorem on hyperplane sections, Ann. of Math. (2) 69 (1959), 713–717.
• [5] V. I. Arnold, On a characteristic class entering into conditions of quantization, Funkcional. Anal. i Priložen. 1 (1967), 1–14, in Russian.
• [6] M. Audin, Fibrés normaux d'immersions en dimension double, points doubles d'immersions lagragiennes et plongements totalement réels, Comment. Math. Helv. 63 (1988), no. 4, 593–623.
• [7] E. Bedford and B. Gaveau, Envelopes of holomorphy of certain $2$-spheres in ${\bf C}\sp{2}$, Amer. J. Math. 105 (1983), no. 4, 975–1009.
• [8] E. Bedford and W. Klingenberg, On the envelope of holomorphy of a $2$-sphere in $\mathbf{C}^{2}$, preprint, 1989.
• [9] E. Bishop, Differentiable manifolds in complex Euclidean space, Duke Math. J. 32 (1965), 1–21.
• [10] S.-S. Chern and E. Spanier, A theorem on orientable surfaces in four-dimensional space, Comment. Math. Helv. 25 (1951), 205–209.
• [11] T. Duchamp and F. Forstnerič, Intersections of totally real and holomorphic disks, preprint, 1991.
• [12] Ya. Eliashberg, Filling by holomorphic discs and its applications, preprint, 1990.
• [13] T. Fiedler, Totally real embeddings of the torus into ${\bf C}\sp 2$, Ann. Global Anal. Geom. 5 (1987), no. 2, 117–121.
• [14] F. Forstenerič, Proper Holomorphic Mappings in Several Complex Variables, thesis, Univ. of Washington, Seattle, 1985.
• [15] F. Forstnerič, On totally real embeddings into ${\bf C}\sp n$, Exposition. Math. 4 (1986), no. 3, 243–255.
• [16] F. Forstnerič, Analytic disks with boundaries in a maximal real submanifold of ${\bf C}\sp 2$, Ann. Inst. Fourier (Grenoble) 37 (1987), no. 1, 1–44.
• [17] F. Forstnerič, A totally real three-sphere in ${\bf C}\sp 3$ bounding a family of analytic disks, Proc. Amer. Math. Soc. 108 (1990), no. 4, 887–892.
• [18] F. Forstnerič and E. L. Stout, A new class of polynomially convex sets, Ark. Mat. 29 (1991), no. 1, 51–62.
• [19] A. B. Givental, Lagrangian imbeddings of surfaces and the open Whitney umbrella, Funktsional. Anal. i Prilozhen. 20 (1986), no. 3, 35–41, 96.
• [20] P. Griffiths and J. Harris, Principles of algebraic geometry, Wiley-Interscience [John Wiley & Sons], New York, 1978.
• [21] M. L. Gromov, Convex integration of differential relations. I, Izv. Akad. Nauk SSSR Ser. Mat. 37 (1973), 329–343, in English, Math. USSR-Izv., 7, (1973), 329–344.
• [22] M. Gromov, Pseudoholomorphic curves in symplectic manifolds, Invent. Math. 82 (1985), no. 2, 307–347.
• [23] M. Gromov, Partial differential relations, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 9, Springer-Verlag, Berlin, 1986.
• [24] V. M. Harlamov and Ya. Eliashberg, On the number of complex points of a real surface in a complex surface, Topology: Proceedings of the International Topological Conference Held in Leningrad, 1982, Lecture Notes in Math., vol. 1060, Springer-Verlag, Berlin, 1983, pp. 143–148.
• [25] F. R. Harvey and R. O. Wells, Jr., Holomorphic approximation and hyperfunction theory on a $C\sp{1}$ totally real submanifold of a complex manifold, Math. Ann. 197 (1972), 287–318.
• [26] L. Hörmander, An introduction to complex analysis in several variables, North-Holland Mathematical Library, vol. 7, North-Holland Publishing Co., Amsterdam, 1990.
• [27] C. E. Kenig and S. M. Webster, The local hull of holomorphy of a surface in the space of two complex variables, Invent. Math. 67 (1982), no. 1, 1–21.
• [28] J. A. Lees, On the classification of Lagrange immersions, Duke Math. J. 43 (1976), no. 2, 217–224.
• [29] W. S. Massey, Proof of a conjecture of Whitney, Pacific J. Math. 31 (1969), 143–156.
• [30] J. W. Milnor and James D. Stasheff, Characteristic classes, Princeton University Press, Princeton, N. J., 1974.
• [31] W. Rudin, Totally real Klein bottles in ${\bf C}\sp{2}$, Proc. Amer. Math. Soc. 82 (1981), no. 4, 653–654.
• [32] A. H. Wallace, Differential topology: first steps, W. A. Benjamin, Inc., Reading, Mass.-London-Amsterdam, 1968.
• [33] S. M. Webster, Minimal surfaces in a Kähler surface, J. Differential Geom. 20 (1984), no. 2, 463–470.
• [34] A. Weinstein, Lectures on Symplectic Manifolds, Reg. Conf. Ser. Math., no. 29, American Mathematical Society, Providence, R.I., 1977.
• [35] R. O. Wells, Jr., Compact real submanifolds of a complex manifold with nondegenerate holomorphic tangent bundles, Math. Ann. 179 (1969), 123–129.
• [36] H. Whitney, The self-intersections of a smooth $n$-manifold in $2n$-space, Ann. of Math. (2) 45 (1944), 220–246.
• [37] F. Forstnerič, Intersections of analytic and smooth discs, preprint, 1991.
• [38] F. W. Kamber and P. Tondeur, Characteristic invariants of foliated bundles, Manuscripta Math. 11 (1974), 51–89.