On the transformation group of a real hypersurface

Webster, S. M.

doi:10.1090/S0002-9947-1977-0481085-5

On the transformation group of a real hypersurface
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by S. M. Webster PDF

Trans. Amer. Math. Soc. 231 (1977), 179-190 Request permission

Abstract:

The group of biholomorphic transformations leaving fixed a strongly pseudoconvex real hypersurface in a complex manifold is a Lie group. In this paper it is shown that the Chern-Moser invariants must vanish if this group is noncompact and the hypersurface is compact. Also considered are transformation groups of flat hypersurfaces and intransitive groups.

References

Elie Cartan, Sur la géométrie pseudo-conforme des hypersurfaces de l’espace de deux variables complexes, Ann. Mat. Pura Appl. 11 (1933), no. 1, 17–90 (French). MR 1553196, DOI 10.1007/BF02417822

Sur la géométrie pseudo-conforme des hypersurfaces de l’espace de deux variables complexes

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S. S. Chern and J. K. Moser, Real hypersurfaces in complex manifolds, Acta Math. 133 (1974), 219–271. MR 425155, DOI 10.1007/BF02392146
Shoshichi Kobayashi, Transformation groups in differential geometry, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 70, Springer-Verlag, New York-Heidelberg, 1972. MR 0355886
N. H. Kuiper, On conformally-flat spaces in the large, Ann. of Math. (2) 50 (1949), 916–924. MR 31310, DOI 10.2307/1969587
Deane Montgomery and Leo Zippin, Existence of subgroups isomorphic to the real numbers, Ann. of Math. (2) 53 (1951), 298–326. MR 47668, DOI 10.2307/1969544
Morio Obata, Conformal transformations of Riemannian manifolds, J. Differential Geometry 4 (1970), 311–333. MR 267485
Morio Obata, The conjectures on conformal transformations of Riemannian manifolds, J. Differential Geometry 6 (1971/72), 247–258. MR 303464
S. M. Webster, Pseudo-Hermitian structures on a real hypersurface, J. Differential Geometry 13 (1978), no. 1, 25–41. MR 520599