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Chen, Bang-Yen

Non-immersion theorems for warped products in complex hyperbolic spaces. (English) Zbl 1018.53024

Proc. Japan Acad., Ser. A 78, No. 6, 96-100 (2002).
Summary: We prove a general optimal inequality for warped products in complex hyperbolic spaces and investigate warped products which satisfy the equality case of the inequality. As immediate applications, we obtain several non-immersion theorems for warped products in complex hyperbolic spaces.

Cited in 1 Review
Cited in 7 Documents

MSC:

53C40 Global submanifolds
53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
53B25 Local submanifolds

Keywords:

inequality; minimal immersion; warped products; complex hyperbolic spaces; non-immersion theorems
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\textit{B.-Y. Chen}, Proc. Japan Acad., Ser. A 78, No. 6, 96--100 (2002; Zbl 1018.53024)
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References:

[1] Chen, B.-Y.: Some pinching and classification theorems for minimal submanifolds. Arch. Math., 60 , 568-578 (1993). · Zbl 0811.53060
[2] Chen, B.-Y.: Geometry of warped product \(CR\)-submanifolds in Kaehler manifolds. Monatsh. Math., 133 , 177-195 (2001); Chen, B.-Y.: Geometry of warped product \(CR\)-submanifolds in Kaehler manifolds, II. Monatsh. Math., 134 , 103-119 (2001). · Zbl 0996.53044
[3] Chen, B.-Y.: On isometric minimal immersions from warped products into real space forms. Proc. Edinburgh Math. Soc. (To appear). · Zbl 1022.53022
[4] Chen, B.-Y., and Ogiue, K.: On totally real submanifolds. Trans. Amer. Math. Soc., 193 , 257-266 (1974). · Zbl 0286.53019
[5] Ejiri, N.: Minimal immersions of Riemannian products into real space forms. Tokyo J. Math., 2 , 63-70 (1979). · Zbl 0441.53044
[6] O’Neill, B.: Semi-Riemannian Geometry with Applications to Relativity. Academic Press, New York (1983).
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