Pseudo-Parallel Legendrian Submanifolds With Flat Normal Bundle of Sasakian Space Forms

Abstract

Let M n be a Legendrian submanifold with flat normal bundle of a Sasakian space form 2 n +1( c ). Further, M n is said to be pseudo-parallel if its second fundamental form h satisfies R ( X, Y ) · h = L ( X ∧ Y · h ) . In this article we shall prove that M is semi-parallel or totally geodesic and if M satisfies L then it is minimal in case of n ≥ 2. Moreover, we show that if M n is also a H-umbilical submanifold then either M n is L = , or n = 1.