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B.-Y. Chen’s inequality for submanifolds of generalized space forms. (English) Zbl 1131.53024
B. Y. Chen introduced so-called $\delta$-invariants for submanifolds of a Riemannian manifold [cf. {\it B. Y. Chen}, Jap. J. Math., New Ser. 26, 105--127 (2000; Zbl 1026.53009)]. Generalized complex space forms and generalized Sasakian space forms have been defined by {\it F. Tricerri} and {\it L. Vanhecke} [Trans. Am. Math. Soc. 267, 365--398 (1981; Zbl 0484.53014)] and by {\it P. Alegre}, {\it D. E. Blair} and {\it A. Carriazo} [Isr. J. Math. 141, 157--183 (2004; Zbl 1064.53026)], respectively. The authors of the present paper investigate sharp inequalities involving $\delta$-invariants for submanifolds of both the generalized complex space forms and the generalized Sasakian space forms.

##### MSC:
 53C40 Global submanifolds (differential geometry) 53B25 Local submanifolds 53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)