A Note on Chen’s Basic Equality for Submanifolds in a Sasakian Space Form
نویسنده
چکیده
It is proved that a Riemannian manifold M isometrically immersed in a Sasakian space form˜M(c) of constant ϕ-sectional curvature c < 1, with the structure vector field ξ tangent to M, satisfies Chen's basic equality if and only if it is a 3-dimensional minimal invariant submanifold. 1. Introduction. Let˜M be an m-dimensional almost contact manifold endowed with an almost contact structure (ϕ,ξ,η), that is, ϕ be a (1, 1)-tensor field, ξ be a vector field, and η be a 1-form, such that ϕ 2 = −I +η⊗ξ and η(ξ) =
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