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 2n+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 thisarticle 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 showthat if M n is also a H-umbilical submanifold then either M n is L = , or n = 1.
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DOI: http://dx.doi.org/10.3968/3002
DOI (PDF): http://dx.doi.org/10.3968/pdf_7
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