Real analytic submanifolds under unimodular transformations

Gong, Xiang Hong

doi:10.1090/S0002-9939-1995-1231299-8

Real analytic submanifolds under unimodular transformations
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Proc. Amer. Math. Soc. 123 (1995), 191-200 Request permission

Abstract:

We study the normal form of totally real and real analytic submanifolds in ${\mathbb {C}^n}$ under holomorphic unimodular transformations. We also consider the unimodular normal form of real surfaces in ${\mathbb {C}^2}$ near an elliptic complex tangent with the non-vanishing Bishop invariant or near a non-exceptional hyperbolic complex tangent.

References

V. I. Arnol′d, On a characteristic class entering into conditions of quantization, Funkcional. Anal. i Priložen. 1 (1967), 1–14 (Russian). MR 0211415, DOI 10.1007/BF01075861
Errett Bishop, Differentiable manifolds in complex Euclidean space, Duke Math. J. 32 (1965), 1–21. MR 200476
Franc Forstnerič, Analytic disks with boundaries in a maximal real submanifold of $\textbf {C}^2$, Ann. Inst. Fourier (Grenoble) 37 (1987), no. 1, 1–44 (English, with French summary). MR 894560, DOI 10.5802/aif.1076
Jürgen Moser, On the volume elements on a manifold, Trans. Amer. Math. Soc. 120 (1965), 286–294. MR 182927, DOI 10.1090/S0002-9947-1965-0182927-5
Jürgen K. Moser and Sidney M. Webster, Normal forms for real surfaces in $\textbf {C}^{2}$ near complex tangents and hyperbolic surface transformations, Acta Math. 150 (1983), no. 3-4, 255–296. MR 709143, DOI 10.1007/BF02392973
J. Vey, Sur le lemme de Morse, Invent. Math. 40 (1977), no. 1, 1–9 (French). MR 453737, DOI 10.1007/BF01389858