Real hypersurfaces in complex Grassmannians of rank two with semi-parallel structure Jacobi operator

TL;DR

This paper proves the nonexistence of real hypersurfaces in complex Grassmannians of rank two with semi-parallel or recurrent structure Jacobi operators, clarifying geometric constraints in these spaces.

Contribution

It establishes the nonexistence of such hypersurfaces with semi-parallel or recurrent structure Jacobi operators in complex Grassmannians of rank two.

Findings

No real hypersurfaces with semi-parallel structure Jacobi operator exist in these spaces.

The nonexistence extends to hypersurfaces with recurrent structure Jacobi operator.

Results contribute to understanding geometric properties of complex Grassmannians.

Abstract

We prove that there does not exist any real hypersurface in complex Grassmannians of rank two with semi-parallel structure Jacobi operator. With this result, the nonexistence of real hypersurface in complex Grassmannians of rank two with recurrent structure Jacobi operator is proved.