Totally real minimal submanifolds in a quaternion projective space

• Autorzy: Ximin Liu
• Języki publikacji: EN

Abstrakty

EN

We prove some pinching theorems with respect to the scalar curvature of 4-dimensional conformally flat (concircularly flat, quasi-conformally flat) totally real minimal submanifolds in QP⁴(c).

Słowa kluczowe

EN

totally real submanifold; quaternion projective space; curvature pinching

Kategorie tematyczne

• 53C42: Immersions (minimal, prescribed curvature, tight, etc.)
• 53C40: Global submanifolds

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1998
• Tom: 69
• Numer: 1
• Strony: 31-36

Daty

wydano

1998

otrzymano

1997-01-06

Twórcy

autor

Ximin Liu

• Department of Mathematics, Nankai University, Tianjin 300071, P.R. China
• Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, P.R. China

Bibliografia

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• [3] S. Ishihara, Quaternion Kählerian manifolds, J. Differential Geom. 9 (1974), 483-500.
• [4] Y. B. Shen, Totally real minimal submanifolds in a quaternion projective space, Chinese Ann. Math. Ser. B 14 (1993), 297-306.
• [5] K. Yano, Concircular geometry I, Proc. Imp. Acad. Sci. Japan Tokyo 16 (1940), 195-200.
• [6] K. Yano and S. Sawaki, Riemannian manifolds admitting a conformal transformation group, J. Differential Geom. 2 (1968), 161-184.