On the intrinsic symmetries of Chen ideal submanifolds

Abstract

Chen ideal submanifolds Mⁿ in Euclidean ambient spaces E^n+m, of arbitrary dimensions n ≥ 2 and codimensions m ≥ 1, at each of their points, do realise an optimal equality between their squared mean curvature (their main extrinsic scalar valued curvature invariant) and their δ (= δ(2)) curvature of Chen (one of their most essential intrinsic scalar valued curvature invariants). In this paper we study the intrinsic symmetry properties related to the Riemann–Christoffel-and conformal Weyl curvatures of such submanifolds.