Symmetries of Wintgen ideal submanifolds

Abstract

Submanifolds M ⁿof all real space forms M̃ ^m+n(c), (n ≥ 2, m ≥ 2) satisfying an equality in the Wintgen inequality ρ ≤ H2 − ρ^⊥ + c at all points of M ⁿ, whereby ρ is normalized scalar curvature of the Riemannian manifold Mⁿ,H2 is the squared mean curvature of the submanifold in M̃ ^m+n(c) and ρ^⊥ is the normalized scalar normal curvature on Mn in M̃ ^m+n(c), are called Wintgen ideal submanifolds. Characterizations based on same basic intrinsic symmetries of such Wintgen ideal submanifolds are given.