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

Xiaomin CHEN

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.

 


Keywords


Legendrian submanifold; Minimal submanifold; H-umbilical submanifold; Pseudo-parallel submanifold; Sasakian space form

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References


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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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