|
Local Cauchy-Riemann embeddability of real hyperboloids into spheres
Author(s):
Jong-Won
Oh
Journal:
Proc. Amer. Math. Soc.
135
(2007),
397-403.
MSC (2000):
Primary 32V30;
Secondary 32V20
Posted:
August 2, 2006
MathSciNet review:
2255286
Retrieve article in:
PDF
Abstract |
References |
Similar articles |
Additional information
Abstract:
In this paper, we study the local Cauchy-Riemann embeddability of strictly pseudoconvex real hyperboloids  into spheres. By solving a CR analogue of the Gauss equation, we prove that  is CR-embeddable into spheres with a CR co-dimension   if and only if it is spherical.
References:
-
- 1.
- Chern, S. S. and Moser, J. K., Real hypersurfaces in complex manifolds, Acta Math. 133 (1974), 219-271. MR 0425155 (54:13112)
- 2.
- Ebenfelt, P., Huang, X. and Zaitsev, D., Rigidity of CR-immersions into spheres, Comm. Anal. Geom. 12 (2004), no. 3, 631-670. MR 2128606 (2006c:53037)
- 3.
- Ebenfelt, P., Huang, X. and Zaitsev, D., The equivalence problem and rigidity for hypersurfaces embedded into hyperquadrics, Amer. J. Math. 127 (2005), no. 1, 169-191. MR 2115664 (2006c:32047)
- 4.
- Faran, J., The nonembeddability of real hypersurfaces in spheres, Proc. Amer. Math. Soc. 103 (1988), 902-904. MR 0947678 (89i:32037)
- 5.
- Forstneric, F., Embedding strictly pseudoconvex domains into balls, Trans. Amer. Math. Soc. 295 (1986), 347-368. MR 0831203 (87k:32052)
- 6.
- Huang, X., On a linearity problem for proper holomorphic maps between balls in complex spaces of different dimensions, J. Differential Geom. 51 (1999), 13-33. MR 1703603 (2000e:32020)
- 7.
- Huang, X. and Ji, S., Mapping
 into  , Invent. Math. 145 (2001), 219-250. MR 1872546 (2002i:32013) - 8.
- Lempert, L., Imbedding Cauchy-Riemann manifolds into a sphere, International J. of Math. 1 (1990), 91-108. MR 1044662 (91c:32013)
- 9.
- Løw, E., Embeddings and proper holomorphic maps of strictly pseudoconvex domains into polydiscs and balls, Math. Z. 190 (1985), 401-410. MR 0806898 (87b:32047)
- 10.
- Stensønes, B., Proper maps which are Lipschitz
 up to the boundary, J. Geom. Anal. 6 (1996), no. 2, 317-339. MR 1469126 (98g:32040) - 11.
- Webster, S. M., Pseudohermitian structures on a real hypersurface, J. Differential Geom. 13 (1978), 25-41. MR 0520599 (80e:32015)
- 12.
- Webster, S. M., The rigidity of C-R hypersurfaces in a sphere, Indiana Univ. Math. J. 28 (1979), 405-416. MR 0529673 (80d:32022)
- 13.
- Webster, S. M., Segre polar correspondence and double valued reflection for general ellipsoids, Analysis and geometry in several complex variables (Katata, 1997), Trends Math., Birkhäuser, Boston, MA (1999), 273-288. MR 1699856 (2000k:32033)
- 14.
- Webster, S. M., A remark on the Chern-Moser tensor, Houston J. Math. 28 (2002), no. 2, 433-435. MR 1898199 (2003d:32047)
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical
Society
with
MSC (2000):
32V30,
32V20
Retrieve articles in all Journals with
MSC (2000):
32V30,
32V20
Additional Information:
Jong-Won
Oh
Affiliation:
Department of Mathematics, Yonsei University, Seoul 120-749, Korea
Address at time of publication:
Department of Mathematics, Seoul National University, San 56-1, Sillim-dong, Gwanak-gu, Seoul 151-742, Korea
Email:
jwoh@math.snu.ac.kr
DOI:
10.1090/S0002-9939-06-08741-7
PII:
S 0002-9939(06)08741-7
Keywords:
CR embeddability,
real hyperboloid,
sphere,
the Gauss equation.
Received by editor(s):
August 25, 2005
Posted:
August 2, 2006
Additional Notes:
The author was supported by BK21-Yonsei University.
Communicated by:
Mei-Chi Shaw
Copyright of article:
Copyright
2006,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
|
