Parallelism on Jacobi Operators for Hopf Hypersurfaces in Complex Two-Plane Grassmannians

Abstract

AbstractIn relation to the generalized Tanaka-Webster connection, we consider a new notion of parallel Jacobi operator for real hypersurfaces in complex two-plane Grassmannians \(G_{2}(\mathbb{C}^{m+2})\) and show results about real hypersurfaces in \(G_{2}(\mathbb{C}^{m+2})\) with generalized Tanaka-Webster parallel structure Jacobi operator and normal Jacobi operator.KeywordsVector FieldCurvature TensorReal HypersurfaceShape OperatorJacobi OperatorThese 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.