Wintgen inequalities on Legendrian submanifolds of generalized Sasakian-space-forms

Abstract

. A submanifold M m of a generalized Sasakian-space-form M 2 n +1 ( f 1 , f 2 ,f 3 ) is said to be C -totally real submanifold if ξ ∈ Γ( T ⊥ M ) and ϕX ∈ Γ( T ⊥ M ) for all X ∈ Γ( TM ). In particular, if m = n , then M n is called Legendrian submanifold. Here, we derive Wintgen inequalities on Legendrian submanifolds of generalized Sasakian-space-forms with respect to different connections; namely, quarter symmetric metric connection, Schouten–van Kampen connection and Tanaka–Webster connection.