Reeb Recurrent Structure Jacobi Operator on Real Hypersurfaces in Complex Two-Plane Grassmannians

Cyclic parallel structure Jacobi operator for real hypersurfaces in complex two-plane Grassmannians

“…for any tangent vector fields X and Y on M (see [19]). From this and using symmetric property of the structure Jacobi operator R ξ in G 2 (C m+2 ), the cyclic parallelism of the structure Jacobi operator (1.4) can be rearranged as follows:…”

Quadratic Killing structure Jacobi operator for real hypersurfaces in complex two-plane Grassmannians

“…for any tangent vector fields X and Y on M (see [11]). From this and using symmetric property of the structure Jacobi operator R ξ in G 2 (C m+2 ), the quadratic Killing structure Jacobi operator ( †) can be rearranged as follows:…”

Structure Lie operator on real hypersurfaces of complex two-plane Grassmannians

“…In addition, if α = g(Aξ, ξ) is not identically zero on M , we say that M has a non-vanishing geodesic Reeb flow. If ξ(α) = 0, we say that the geodesic Reeb flow is constant along the Reeb direction (see [9]). We denote by D ⊥ the distribution defined by D ⊥ = Span {ξ 1 , ξ 2 , ξ 3 } and by D its orthogonal complement distribution.…”