DOI QR코드

DOI QR Code

On G-invariant Minimal Hypersurfaces with Constant Scalar Curvatures in S5

  • So, Jae-Up (Department of Mathematics and Institute of Pure and Applied Mathematics, Chonbuk National University)
  • 투고 : 2012.07.25
  • 심사 : 2012.08.23
  • 발행 : 2013.12.23

초록

Let $G=O(2){\times}O(2){\times}O(2)$. Then a closed G-invariant minimal hypersurface with constant scalar curvature in $S^5$ is a product of spheres, i.e., the square norm of its second fundamental form, S = 4.

키워드

과제정보

연구 과제 주관 기관 : Chonbuk National University

참고문헌

  1. S. Chang, On minimal hypersurfaces with constant scalar curvatures in $S^4$, J. Diff. Geom., 37(1993), 523-534. https://doi.org/10.4310/jdg/1214453898
  2. S. S. Chern, M. do Carmo and S. Kobayashi, Minimal submanifolds of a sphere with second fundamental form of constant length, Duke Math. J., 61(1990), 195-206. https://doi.org/10.1215/S0012-7094-90-06109-5
  3. W. Y. Hsiang, On the construction of in nitely many congruence classes of imbedded closed minimal hypersurfaces in $S^n$(1) for all $n{\geq}3$, Duke Math. J., 55(2)(1987), 361-367. https://doi.org/10.1215/S0012-7094-87-05520-7
  4. H. B. Lawson, Local rigidity theorems for minimal hypersurfaces, Annals of Math., 89(1969), 187-191. https://doi.org/10.2307/1970816
  5. C. K. Peng and C. L. Terng, Minimal hypersurface of spheres with constant scalar curvature, Annals of Math. Studies, No. 103, Princeton University Press, Princeton, NJ, (1983), 177-198.
  6. J. Simons, Minimal varieties in a Riemannian manifold, Ann. of Math., 88(1968), 62-105. https://doi.org/10.2307/1970556
  7. J. U. So, On G-invariant Minimal Hypersurfaces with Constant Scalar Curvatures in $S^5$, Commun. Korean Math. Soc., 17(2002), 261-278. https://doi.org/10.4134/CKMS.2002.17.2.261
  8. H. Yang and Q. M. Cheng, Chern's conjecture on minimal hypersurfaces, Math. Z., 227(1998), 377-390. https://doi.org/10.1007/PL00004382
  9. S. T. Yau, Problem section, Annals of Math. Studies, No. 102, Princeton University Press, Princeton, NJ, (1982), 693.