Miscellanea

Abstract

Totally umbilical submanifolds of complex space forms have been classified by B.Y. Chen&K. Ogiue, [60], cf. Theorem 1, p. 225. Their classification relies on the earlier observation (cf. [59], Prop. 3.1, p. 260) that curvature-invariant submanifolds of a complex space form are either holomorphic or totally real. In [79] one extends these ideas to submanifolds of Sasakian space forms and obtains the following:Theorem 17.1 Let M2m+1 be an odd-dimensional totally umbilical sub-manifold of a Sasakian space form M2m+1(c), 1 < m < n. If M2m+1 is tangent to the contact vector ξ of M2n+1(c) then M2m+1 is a Sasakian space form immersed in M2n+1(c) as a totally geodesic submanifold.KeywordsSectional CurvatureFundamental FormHermitian ManifoldComplex Space FormCosymplectic ManifoldThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.