Remote Access Conformal Geometry and Dynamics
Green Open Access

Conformal Geometry and Dynamics

ISSN 1088-4173

 
 

 

The space-like surfaces with vanishing conformal form in the conformal space


Author: Changxiong Nie
Journal: Conform. Geom. Dyn. 16 (2012), 204-208
MSC (2010): Primary 53A30, 53C50
DOI: https://doi.org/10.1090/S1088-4173-2012-00247-0
Published electronically: August 15, 2012
MathSciNet review: 2958931
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The conformal geometry of surfaces in the conformal space $ \mathbf {Q}^n_1$ is studied. We classify the space-like surfaces in $ \mathbf {Q}^n_1$ with vanishing conformal form up to conformal equivalence.


References [Enhancements On Off] (What's this?)

  • 1. Wang, C.P., Moebius geometry of submanifolds in $ S^n$, Manuscripta Math. 96 (1998), 517-534. MR 1639852 (2000a:53019)
  • 2. Li, H.Z., Wang, C.P., Surfaces with vanishing Moebius form in $ \mathbb{S}^n$, Acta Math. Sinica, Engl. Ser. 19 (2003), 671-678. MR 2023361 (2004j:53076)
  • 3. Bryant, R.L., Minimal surfaces of constant curvature in $ \mathbb{S}^n$, Trans. Amer. Math. Soc. 290 (1985), 259-271. MR 787964 (87c:53110)
  • 4. Deng, Y.J., Wang, C.P., Willmore surfaces in Lorentzian space, Sci. China Ser. A 35 (2005), 1361-1372.
  • 5. Nie, C.X., Ma, X., Wang, C.P., Conformal CMC-surfaces in Lorentzian space forms, Chin. Ann. Math., Ser. B, 28 (2007), 299-310. MR 2339435 (2008e:53022)
  • 6. Alias, L.J., Palmer, B., Conformal geometry of surfaces in Lorentzian space forms, Geometriae Dedicata 60 (1996), 301-315. MR 1384435 (97f:53099)
  • 7. Nie, C.X., Li, T.Z., He, Y.J., Wu, C.X., Conformal isoparametric hypersurfaces with two distinct conformal principal curvatures in conformal space, Sci. China Ser. A 53 (2010), 953-965. MR 2640180 (2011c:53133)
  • 8. Blaschke, W., Vorlesungen über Differentialgeometrie, Vol. 3, Springer, Berlin, 1929.
  • 9. Hertrich-Jeromin, U., Introduction to Möbius Differential Geometry, London Math. Soc. Lecture Note Series, Vol. 300, Cambridge University Press, Cambridge, 2003. MR 2004958 (2004g:53001)
  • 10. O'Neill, B., Semi-Riemannian Geometry with Applications to Relativity, Pure and Applied Mathematics, 103, Academic Press, New York, 1983. MR 719023 (85f:53002)

Similar Articles

Retrieve articles in Conformal Geometry and Dynamics of the American Mathematical Society with MSC (2010): 53A30, 53C50

Retrieve articles in all journals with MSC (2010): 53A30, 53C50


Additional Information

Changxiong Nie
Affiliation: Faculty of Mathematics and Computer Sciences, Hubei University, Wuhan 430062, People’s Republic of China
Email: chxnie@163.com

DOI: https://doi.org/10.1090/S1088-4173-2012-00247-0
Received by editor(s): July 29, 2011
Published electronically: August 15, 2012
Additional Notes: This work was partially supported by National Natural Science Foundation of China (Grant Nos. 10971055 and 10801006) and Zhongdian Natural Science Foundation of Hubei Educational Committee
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society