References
K. Benko, M. Kothe, K. D. Semmler andU. Simon, Eigenvalues of the Laplacian and Curvature. Colloq. Math.42, 19–31 (1979).
B. Y. Chen andC. S. Houh, Totally Real Submanifolds of a Quaternion Projective Space. Ann. Mat. Pura Appl.120, 185–199 (1979).
S. S.Chern, M.do Carmo and S.Kobayashi, Minimal Submanifolds of a Sphere with Second Fundamental Form of Constant Length. Shiing-shen Chern Selected Papers, 393–409, Berlin-Heidelberg-New York 1978.
Y. B. Shen, On Intrinsic Rigidity for Minimal Submaifolds in a Sphere. Scie. China (Ser. A),32, 769–781 (1989).
Y. B. Shen, Totally Real Minimal Submanifolds in a Quaternion Projective Space. Preprint, Hangzhou University, China 1988.
B.Wu and H.Song, 3-dimensional Minimal Submanifolds of a Sphere. Acta Math. Sinica, to appear (Chinese).
G. Wu andW. Chen, An Inequality for Matrices and Its Applications in Geometry. Acta Math. Sinica (3)31, 348–355, 1988 (Chinese).
G.Zhao, A Rigidity Theorem for Totally Real Minimal Submanifolds in a Complex Projective Space. J. Sichuan Univ., to appear.
Author information
Authors and Affiliations
Additional information
Research supported by the National Natural Science Foundation of China, the ‘Tianyuan’ Foundation of China.
Rights and permissions
About this article
Cite this article
An-Min, L., Jimin, L. An intrinsic rigidity theorem for minimal submanifolds in a sphere. Arch. Math 58, 582–594 (1992). https://doi.org/10.1007/BF01193528
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01193528