Global Journal of Pure and Applied Mathematics. ISSN 0973-1768 Volume 16, Number 3 (2020), pp. 419-429 c Research India Publications http://www.ripublication.com/gjpam.htm f-Biharmonic Submanifolds in S-Space Form Najma Abdul Rehman Mathematics Department Comsats University Islamabad, Sahiwal Campus, Pakistan E-mail: najma - ar@hotmail.com Abstract Complex and contact structures are generalized in the form of S-manifolds. In this paper we have studied f-biharmonic submanifolds in S-space form and have derived condition on second fundamental form for f-biharmonic submanifolds. 2010 AMS Mathematics Subject Classification: 58E20, 53C43, 53C55. Keywords and phrases: Biharmonic maps, f-biharmonic submanifolds, S-space forms. 1. INTRODUCTION Harmonic maps are important field of research being the critical points of energy fuctional. Due to both geometric and analytical aspects, harmonic maps are attractive field of research. The idea behind the biharmonic maps is old and is attractive subject of research. They have been studied since 1862 by Maxwell and Airy to describe a mathematical model of elasticity. Biharmonic maps are generalization of harmonic maps and first regular studied by J. Eells and L. Lemair in 1983 [4]. In 1986 G. Y. Jiang [6] discussed first and second variations formulas for bienergy functional. After this many authors studied biharmonic maps and biharmonic submanifolds etc. [2], [5], [10],[11],[12]. Lichnerowicz gave idea of f-biharmonic maps [7]. Many authors studied the f-biharmonic submanifolds for complex space form and generalized Sasakian space forms separately [8], but after the generalization of complex and contact space forms as S-space forms [1], it is natural to study f-biharmonic maps on S-space forms. After introduction, second section contains basics of f-biharmonic maps and S-space forms. Third section consists of main results.