A construction of curvature-adapted hypersurfaces in the product of symmetric spaces

Naoyuki Koike

paper

A construction of curvature-adapted hypersurfaces in the product of symmetric spaces

arXiv:2503.23917

Abstract

In this paper, we give a construction of curvature-adapted hypersurfaces in the product $G_{1} / K_{1} \times G_{2} / K_{2}$ of (Riemannian) symmetric spaces $G_{i} / K_{i}$ ( $i = 1, 2$ ). By this construction, we obtain many examples of curvature-adapted hypersurfaces in $G_{1} / K_{1} \times G_{2} / K_{2}$ . Also, we calculate the eigenvalues of the shape operator and the normal Jacobi operator of the curvature-adapted hypersurfaces obtained by this construction.

13 pages