Jacobi operators along the structure flow on real hypersurfaces in a nonflat complex space form II
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Let M be a real hypersurface of a complex space form with almost contact metric structure (ø, ξ, ŋ, g). In this paper, we study real hypersurfaces in a complex space form whose structure Jacobi operator R_ξ=R(· , ξ)ξ is ξ-parallel. In particular, we prove that the condition ∇_ξR_ξ=0 characterizes the homogeneous real hypersurfaces of type A in a complex projective space or a complex hyperbolic space when R_ξØS=R_ξSØ holds on M, where S denotes the Ricci tensor of type (1,1) on M.
Abstract
Let M be a real hypersurface of a complex space form with almost contact metric structure (ø, ξ, ŋ, g). In this paper, we study real hypersurfaces in a complex space form whose structure Jacobi operator R_ξ=R(· , ξ)ξ is ξ-parallel. In particular, we prove that the condition ∇_ξR_ξ=0 characterizes the homogeneous real hypersurfaces of type A in a complex projective space or a complex hyperbolic space when R_ξØS=R_ξSØ holds on M, where S denotes the Ricci tensor of type (1,1) on M.
참고문헌 (14)
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