60 citations · 196 across the 20 of their papers we have counts for
13 papers · 1 filter
Volume minimization and obstructions to solving some problems in Kähler geometry
Akito Futaki, Hajime Ono
There is an obstruction to the existence of Kähler -Einstein metrics which is used to define the GIT weight for K-stability, and it has been extended to various geometric problems.…
On the existence problem of Einstein-Maxwell Kähler metrics
Akito Futaki, Hajime Ono
In this expository paper we review on the existence problem of Einstein-Maxwell Kähler metrics, and make several remarks. Firstly, we consider a slightly more general set-up than E…
Cahen-Gutt moment map, closed Fedosov star product and structure of the automorphism group
Akito Futaki, Hajime Ono
We show that if a compact Kaehler manifold of non-negative Ricci curvature admits closed Fedosov star product then the reduced Lie algebra of holomorphic vector fields on i…
Conformally Einstein-Maxwell Kähler metrics and structure of the automorphism group
Akito Futaki, Hajime Ono
Let be a compact Kähler manifold and a positive smooth function such that its Hamiltonian vector field for the Kähler form is a holomorph…
Volume minimization and Conformally Kähler, Einstein-Maxwell geometry
Akito Futaki, Hajime Ono
Let be a compact complex manifold admitting a Kähler structure. A conformally Kähler, Einstein-Maxwell metric (cKEM metric for short) is a Hermitian metric on w…
Almost all Lagrangian torus orbits in are not Hamiltonian volume minimizing
Hiroshi Iriyeh, Hajime Ono
All principal orbits of the standard Hamiltonian -action on the complex projective space are Lagrangian tori.In this article, we prove that most of them are n…
Almost all standard Lagrangian tori in C^n are not Hamiltonian volume minimizing
Hiroshi Iriyeh, Hajime Ono
In 1993, Y.-G. Oh proposed a problem whether standard Lagrangian tori in C^n are volume minimizing under Hamiltonian isotopies of C^n. In this article, we prove that most of them d…
An example of asymptotically Chow unstable manifolds with constant scalar curvature
Hajime Ono, Yuji Sano, Naoto Yotsutani
Donaldson proved that if a polarized manifold has constant scalar curvature Kähler metrics in and its automorphism group Aut is discrete, is asympto…
Einstein metrics and GIT stability
Akito Futaki, Hajime Ono
In this expository article we review the problem of finding Einstein metrics on compact Kähler manifolds and Sasaki manifolds. In the former half of this article we see that, in th…
Hilbert series and obstructions to asymptotic semistability
Akito Futaki, Hajime Ono, Yuji Sano
Given a polarized manifold there are obstructions for asymptotic Chow semistability described as integral invariants. One of them is an obstruction to the existence for the first C…
Uniqueness and examples of compact toric Sasaki-Einstein metrics
Koji Cho, Akito Futaki, Hajime Ono
In [11] it was proved that, given a compact toric Sasaki manifold of positive basic first Chern class and trivial first Chern class of the contact bundle, one can find a deformed S…
Transverse Kähler geometry of Sasaki manifolds and toric Sasaki-Einstein manifolds
Akito Futaki, Hajime Ono, Guofang Wang
In this paper we study compact Sasaki manifolds in view of transverse Kähler geometry and extend some results in Kähler geometry to Sasaki manifolds. In particular we define integr…
Integral Geometry and Hamiltonian volume minimizing property of a totally geodesic Lagrangian torus in S^2 times S^2
Hiroshi Iriyeh, Hajime Ono, Takashi Sakai
We prove that the product of equators in is globally volume minimizing under Hamiltonian deformations.