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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 δ-invariants for submanifolds of a Riemannian manifold [cf. 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 F. Tricerri and L. Vanhecke [Trans. Am. Math. Soc. 267, 365–398 (1981; Zbl 0484.53014)] and by P. Alegre, D. E. Blair and A. Carriazo [Isr. J. Math. 141, 157–183 (2004; Zbl 1064.53026)], respectively. The authors of the present paper investigate sharp inequalities involving δ-invariants for submanifolds of both the generalized complex space forms and the generalized Sasakian space forms.
MSC:
53C40Global submanifolds (differential geometry)
53B25Local submanifolds
53C25Special Riemannian manifolds (Einstein, Sasakian, etc.)