• 대한수학회지
• /
• 제61권2호
• /
• pp.309-339
• /
• 2024

Let M be a real hypersurface in the complex hyperbolic quadric Q^m*, m ≥ 3. The Riemannian curvature tensor field R of M allows us to define a symmetric Jacobi operator with respect to the Reeb vector field ξ, which is called the structure Jacobi operator R_ξ = R( · , ξ)ξ ∈ End(TM). On the other hand, in [20], Semmelmann showed that the cyclic parallelism is equivalent to the Killing property regarding any symmetric tensor. Motivated by his result above, in this paper we consider the cyclic parallelism of the structure Jacobi operator R_ξ for a real hypersurface M in the complex hyperbolic quadric Q^m*. Furthermore, we give a complete classification of Hopf real hypersurfaces in Q^m* with such a property.

• 호남수학학술지
• /
• 제16권1호
• /
• pp.17-22
• /
• 1994

• 대한수학회지
• /
• 제27권1호
• /
• pp.47-67
• /
• 1990

• 대한수학회논문집
• /
• 제7권1호
• /
• pp.99-110
• /
• 1992

• 대한수학회지
• /
• 제32권3호
• /
• pp.509-518
• /
• 1995

Let $M^n$ be a hypersurface in the Euclidean space $R^{n+1}$ with position vector field x and unit normal vector field G.

• 대한수학회지
• /
• 제26권2호
• /
• pp.311-322
• /
• 1989

• Kyungpook Mathematical Journal
• /
• 제30권2호
• /
• pp.127-135
• /
• 1990

• 대한수학회지
• /
• 제29권1호
• /
• pp.63-77
• /
• 1992

• 대한수학회지
• /
• 제12권1호
• /
• pp.63-70
• /
• 1975

• 대한수학회지
• /
• 제31권3호
• /
• pp.429-437
• /
• 1994

Let $M^n$ be a connected hypersurface in Euclidean (n + 1)-space $E^{n+1}$, and let $G : G^n \longrightarrow S^n(1) \subset E^{n+1}$ be its Gauss map.