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Certain inequalities for submanifolds in \((K,\mu)\)-contact space forms. (English) Zbl 1002.53029

In the paper under review the authors obtain sharp relationships between the Ricci curvature and the squared mean curvature for submanifolds in \( (K, \mu) \) contact space forms.

MSC:

53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
53D20 Momentum maps; symplectic reduction
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References:

[1] Koufogiorgos, Geometry and topology of submanifolds 8 pp 195– (1995)
[2] Defever, Boll. Un. Mat. Ital. 11 pp 365– (1997)
[3] DOI: 10.1017/S0017089599970271 · Zbl 0962.53015 · doi:10.1017/S0017089599970271
[4] Chen, Japan. J. Math. 26 pp 105– (2000)
[5] DOI: 10.1007/BF02761646 · Zbl 0837.53038 · doi:10.1007/BF02761646
[6] Blair, Contact manifolds in Riemannian heometry 509 (1976) · Zbl 0319.53026 · doi:10.1007/BFb0079307
[7] DOI: 10.1007/BF01236084 · Zbl 0811.53060 · doi:10.1007/BF01236084
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