## Duke Mathematical Journal

### Equivalence of real submanifolds under volume-preserving holomorphic automorphisms of $\mathbf{C}^n$

Franc Forstneric

#### Article information

Source
Duke Math. J. Volume 77, Number 2 (1995), 431-445.

Dates
First available in Project Euclid: 20 February 2004

https://projecteuclid.org/euclid.dmj/1077286348

Digital Object Identifier
doi:10.1215/S0012-7094-95-07713-8

Mathematical Reviews number (MathSciNet)
MR1321065

Zentralblatt MATH identifier
0831.32009

#### Citation

Forstneric, Franc. Equivalence of real submanifolds under volume-preserving holomorphic automorphisms of C n . Duke Math. J. 77 (1995), no. 2, 431--445. doi:10.1215/S0012-7094-95-07713-8. https://projecteuclid.org/euclid.dmj/1077286348.

#### References

• [1] R. Abraham and J. E. Marsden, Foundations of Mechanics, 2nd ed., Benjamin, Reading, 1978.
• [2] E. Andersén, Volume-preserving automorphisms of ${\bf C}\sp n$, Complex Variables Theory Appl. 14 (1990), no. 1-4, 223–235.
• [3] E. Andersén and L. Lempert, On the group of holomorphic automorphisms of ${\bf C}\sp n$, Invent. Math. 110 (1992), no. 2, 371–388.
• [4] R. Bott and W. L. Tu, Differential Forms in Algebraic Topology, Graduate Texts in Math., vol. 82, Springer-Verlag, New York, 1982.
• [5] F. Forstneric, Approximation by automorphisms on smooth submanifolds of $\mathbf{C} ^n$, to appear in Math. Ann.
• [6] F. Forstneric, Actions of $(\mathbf{R}, +)$ and $(\mathbf{C}, +)$ on complex manifolds, to appear in Math. Z.
• [7] F. Forstneric, A theorem in complex symplectic geometry, to appear in J. of Geom. Anal.
• [8] F. Forstneric and J.-P. Rosay, Approximation of biholomorphic mappings by automorphisms of ${\bf C}^n$, Invent. Math. 112 (1993), no. 2, 323–349.
• [9] H. Grauert and R. Remmert, Theory of Stein Spaces, Grundlehren Math. Wiss., vol. 236, Springer-Verlag, Berlin, 1979.
• [10] R. C. Gunning and H. Rossi, Analytic Functions of Several Complex Variables, Prentice Hall, Englewood Cliffs, 1965.
• [11] L. Hörmander, An Introduction to Complex Analysis in Several Variables, 3rd ed., North-Holland Mathematical Library, vol. 7, North-Holland, Amsterdam, 1990.
• [12] R. M. Range and Y.-T. Siu, $C\sp{k}$ approximation by holomorphic functions and $\bar \partial$-closed forms on $C\sp{k}$ submanifolds of a complex manifold, Math. Ann. 210 (1974), 105–122.
• [13] J.-P. Rosay, Straightening of arcs, Astérisque (1993), no. 217, 217–225, Colloque d'analyse complexe et géométrie, Marseille, 1992.
• [14] J.-P. Rosay and W. Rudin, Holomorphic maps from ${\bf C}\sp n$ to ${\bf C}\sp n$, Trans. Amer. Math. Soc. 310 (1988), no. 1, 47–86.