The Principal Extrinsic and Intrinsic Tangent Directions of GeneralisedWintgen Ideal Legendrian Submanifolds

Abstract:

For Legendrian submanifolds Mn in Sasakian space forms ∼M 2n+1 (c), I. Mihai obtained an inequality relating (intrinsic) the normalised scalar curvature and (extrinsic) squared mean curvature and normalised normal curvature of M in ∼M , characterising also the corresponding equality case. In this paper, it’s shown that (intrinsic) Ricci principal directions and (extrinsic) Casorati principal directions, for generalised Wintgen ideal Legendrian submanifolds Mn in Sasakian space forms ∼M 2n+1 (c), do coincide.