On $f$-Biminimal Legendre Curves in $(\alpha ,\beta )$-Trans Sasakian Generalized Sasakian Space Forms

Abstract

In this paper, $f$-biminimal Legendre curves are studied in $(\protect\alpha ,\protect\beta )$-trans Sasakian generalized Sasakian space forms. Necessary and sufficient conditions are obtained for a Legendre curve to be $f$-biminimal in such space forms . Besides, some special cases are studied and some nonexistence theorems are obtained.