Waseda Young Researchers Meeting on Geometry 2026

Abstract: Killing spinors are special sections of the spinor bundle on spin manifolds. In standard spin geometry, we consider spin-1/2 spinor fields. In this talk, we define a higher-spin (spin-3/2, spin-5/2, ...) version of Killing spinors and study them in detail in dimension three. We also give explicit expressions of higher-spin Killing spinors on the 3-sphere and the hyperbolic 3-space. This is joint work with Yasushi Homma and Soma Ohno.

Abstract: In this talk, we discuss several completeness conditions for globally hyperbolic spacetimes within the framework of low-regularity settings. These conditions, originally introduced by Busemann and Beem, serve as Lorentzian analogues to those found in the classical Hopf-Rinow theorem. As a related result, we explain an approximation theorem for the space of Cauchy hypersurfaces, a space whose properties have recently been investigated by Lange and Peteranderl.

Abstract: For immersions of compact n-dimensional manifolds into Euclidean spaces, the total absolute curvature is a global geometric quantity defined by integrating the absolute value of the Lipschitz–Killing curvature. The Chern–Lashof theorem states that the total absolute curvature is bounded below by the sum of the Betti numbers. Moreover, it is equal to 2 if and only if the image is a convex hypersurface embedded in an (n+1)-dimensional affine subspace. In 2001, Koike introduced the total absolute curvature for equiaffine immersions of arbitrary dimension and codimension, and established a Chern–Lashof type inequality. However, a geometric characterization of the case in which the total absolute curvature attains its minimum value had remained unknown in the equiaffine setting. In this talk, I investigate the relationship between the minimality of the total absolute curvature and convexity for equiaffine immersions, without assuming the non-degeneracy of the affine fundamental form. I prove that the total absolute curvature is equal to 2 if and only if the image is a convex hypersurface embedded in an (n+1)-dimensional affine subspace.

Abstract: We study the existence of Mabuchi solitons on admissible manifolds as defined by Apostolov--Calderbank--Gauduchon--Tønnesen-Friedman. We prove that a Fano admissible manifold admits a Mabuchi soliton if and only if the Mabuchi constant is less than 1. We also provide an explicit formula for the Mabuchi constant on Fano admissible manifolds, which generalizes that of Mabuchi. Using this formula, we completely determine the existence and non-existence of Mabuchi solitons on Fano admissible manifolds over the complex projective space. This is joint work with Yasufumi Nitta.

Abstract: Γ-symmetric spaces were first defined by R. Lutz in 1981 as a generalization of symmetric spaces. Roughly speaking, they are manifolds that possess a transformation group, at each point, isomorphic to a finite abelian group Γ. In this talk, we introduce the definition of (Riemannian) Γ-symmetric spaces and consider their products and decompositions. Generally, there can be multiple Γ-symmetric product structures on a product manifold of given Γ-symmetric spaces. On the other hand, there exists an example of a Riemannian Γ-symmetric space that satisfies the following property: when it is decomposed into two Riemannian Γ-symmetric spaces, the original space is not the product of the two as Riemannian manifolds, even though it is a product as Γ-symmetric spaces (without metrics). We observe these phenomena, which do not appear when we only consider standard symmetric spaces.

Abstract: In geometry, studying whether a given Lie group admits a special left-invariant geometric structure is crucial.  In our previous work, we constructed nilpotent Lie algebras from finite quivers without cycles by utilizing paths within these quivers. Furthermore, we proved that the simply-connected Lie groups corresponding to these nilpotent Lie algebras always admit left-invariant Ricci solitons. In this talk, we extend our approach by constructing solvable Lie algebras from finite quivers without cycles, adding vertices as paths of length zero. We demonstrate that the simply-connected Lie groups corresponding to these solvable Lie algebras always admit left-invariant Ricci solitons. Additionally, we prove that if a quiver is an  oriented multi-tree, the Ricci soliton Lie group obtained by this quiver admits a left-invariant metric which is isometric to the direct product of a flat metric and an Einstein metric.