arXiv subjects

Yuuki Sasaki

Publications and source records attributed to Yuuki Sasaki.

5 recordsLinked to original sources

arXiv2026

A Unified Construction of Exceptional Symmetric Spaces

We present a unified construction of all simply connected irreducible exceptional compact symmetric spaces as totally geodesic submanifolds of $E_{8}$. Using this construction, we obtain a unified description of totally geodesic embeddings between exceptional symmetric spaces by determining all inclusion relations among them. The resulting inclusion structure exhibits a remarkable and unexpected symmetry, suggesting a deeper geometric relationship among exceptional symmetric spaces.

math.DG↗

arXiv2025

Antipodal sets of exceptional symmetric spaces

In this paper, we study maximal antipodal sets in simply connected exceptional compact symmetric spaces. Combining our results with the existing literature, we obtain a complete classification of maximal antipodal sets in all such spaces. Moreover, through the description of antipodal sets, we disscus the inclusion relations among exceptional symmetric spaces.

math.DG↗

arXiv2025

On cohomogeneity one hyperpolar actions related to $G_{2}$

Cohomogeneity one actions on irreducible Riemannian symmetric spaces of compact type are classified into three cases: Hermann actions, actions induced by the linear isotropy representation of a Riemannian symmetric space of rank 2, and exceptional actions. In this paper, we consider exceptional actions related to the exceptional compact Lie group $G_{2}$ and investigate some properties of their orbits as Riemannian submanifolds. In particular, we examine the principal curvatures of principal orbits and classify principal orbits that are minimal, austere, weakly reflective, and proper biharmonic.

math.DG↗

arXiv2025

Sasaki-Einstein orbits in compact Hermitian symmetric spaces

The aim of the present papar is to study the orbits of the isotropy gourp action on an irreducible Hermitian symmetric space of compact type. Specifically, we examine the properties of these orbits as {\it CR} submanifolds of a Kähler manifold. Our focus is on the leaves of the totally real distribution, and we investigate the properties of leaves as a Riemannian submanifold. In particular, we prove that any leaf is a totally geodesic submanifold of the orbit. Additionally, we explore the conditions under which each leaf becomes a totally geodesic submanifold of the ambient space. The integrability of the complex distribution is also studied. Moreover, we analyze a contact structure of orbits where the rank of the totally real distribution is 1. We obtain a classification of the orbits that possess either a contact structure or a Sasakian structure compatible with the complex structure on the ambient space. Furthermore, we classify those Sasaki orbits that are Einstein with respect to the induced metric. Specifically, we completely detemine Sasaki-Einstein orbits.

math.DG↗

arXiv2025

An example of non-compact totally complex submanifolds of compact quaternionic Kähler symmetric spaces

Totally complex submanifolds of a quaternionic Kähler manifold are analogous to complex submanifolds of a Kähler manifold. In this paper, we construct an example of a non-compact totally complex submanifold of maximal dimension of a compact quaternionic Kähler symmetric space, except for quaternionic projective spaces. A compact Lie group acts on our example isometrically, and this action is of cohomogeneity one. Our example is a holomorphic line bundle over some Hermitian symmetric space of compact type. Moreover, each fiber is a totally geodesic submanifold of the ambient quaternionic Kähler symmetric space and our example is a ruled submanifold. Our construction relies on the action of a subgroup of the isometry group and a maximal totally geodesic sphere with maximal sectional curvature known as a Helgason sphere. Furthermore, we prove that there exist no compact submanifolds of the same dimension that contain our example as an open part, except where the ambient quaternionic Kähler symmetric space is a complex Grassmannian.

math.DG↗