Chen inequalities for submanifolds of complex space forms and Sasakian space forms endowed with semi-symmetric metric connections (Q640278)

Chen inequalities are usually considered for submanifolds of some manifolds endowed with a Levi-Civita connection. In a previous paper [Taiwanese J. Math. 14, No.~4, 1465--1477 (2010; Zbl 1217.53055)], the authors obtained some Chen inequalities for submanifolds of a real space form endowed with a semi-symmetric metric connection. In the present paper, they obtain Chen inequalities for submanifolds immersed in a complex space-form or in a Sasakian space-form, both endowed with a semi-symmetric metric connection. The whole study is based on a well known relation between the Levi-Civita connection and a semi-symmetric metric connection established by \textit{K. Yano} [Rev. Roum. Math. Pures Appl. 15, 1579--1586 (1970; Zbl 0213.48401)].