Related papers: Geodesic-Einstein metrics and nonlinear stabilitie…

We study a variational problem on a smooth manifold with a decomposition of the tangent bundle into $k>2$ subbundles (distributions), namely, we consider the integrated sum of their mixed scalar curvatures as a functional of adapted…

We establish the essentially optimal form of Donaldson's geodesic stability conjecture regarding existence of constant scalar curvature K\"ahler metrics. We carry this out by exploring in detail the metric geometry of Mabuchi geodesic rays,…

In this paper, we introduce a family of generalized Donaldson's functional on holomorphic vector bundles, whose Euler-Lagrange equations are a vector bundle version of the complex $k$-Hessian equations. We also discuss the uniqueness of…

We prove a central limit theorem for smooth linear statistics associated with zero divisors of standard Gaussian holomorphic sections in a sequence of holomorphic line bundles with Hermitian metrics of class $\mathscr{C}^{3}$ over a compact…

In this paper we describe an approach to complex Finsler metrics suitable to deal with global questions, and stressing the similarities between hermitian and complex Finsler metrics. Let $F$ be a smooth complex Finsler metric on a complex…

We study scalar-tensor theories respecting the projective invariance in the metric-affine formalism. The metric-affine formalism is a formulation of gravitational theories such that the metric and the connection are independent variables in…

We consider a homogeneous fibration $G/L \to G/K$, with symmetric fiber and base, where $G$ is a compact connected semisimple Lie group and $L$ has maximal rank in $G$. We suppose the base space $G/K$ is isotropy irreducible and the fiber…

We introduce a metric on Hilbert modules equipped with a generalized form of a differential structure, thus extending Gromov-Hausdorff convergence theory to vector bundles and quantum vector bundles --- not convergence as total space but…

We apply Ueda theory to a study of singular Hermitian metrics of a (strictly) nef line bundle $L$. Especially we study minimal singular metrics of $L$, metrics of $L$ with the mildest singularities among singular Hermitian metrics of $L$…

We investigate principal $G$-bundles on a compact K\"ahler manifold, where $G$ is a complex algebraic group such that the connected component of it containing the identity element is reductive. Defining (semi)stability of such bundles, it…

We study Einstein metrics on complex projective spaces that are invariant under cohomogeneity one actions of compact connected Lie groups, under the assumption that the singular orbits are totally geodesic. These actions were classified by…

In this thesis we study the relationship between the existence of canonical metrics on a complex manifold and stability in the sense of geometric invariant theory. We introduce a modification of K-stability of a polarised variety which we…

In this article we investigate a type of totally geodesic map which has its image being a geodesic in an anisotropic Riemannian manifold. We consider its nonlinear stability among the family of wave maps. We first establish the…

We investigate the formal principle for holomorphic line bundles on neighborhoods of an analytic subset of a complex manifold mainly in the case where it can be realized as an open subset of a compact K\"ahler manifold. Our approach…

We review the notions of (weak) Hermitian-Yang-Mills structure and approximate Hermitian-Yang-Mills structure for Higgs bundles. Then, we construct the Donaldson functional for Higgs bundles over compact K\"ahler manifolds and we present…

Alan Weinstein showed that certain characteristic numbers of any Riemannian submersion with totally geodesic fibers and positive vertizontal curvatures are nonzero. In this paper we explicitly compute these invariants in terms of Chern and…

Any $6$-dimensional strict nearly K\"ahler manifold is Einstein with positive scalar curvature. We compute the coindex of the metric with respect to the Einstein-Hilbert functional on each of the compact homogeneous examples. Moreover, we…

Bryant and Salamon gave a construction of metrics of G2 holonomy on the total space of the bundle of anti-self-dual (ASD) 2-forms over a 4-dimensional self-dual Einstein manifold. We generalise it by considering the total space of an SO(3)…

We consider Heisenberg groups equipped with a sub-Finsler metric. Using methods of optimal control theory we prove that in this geometric setting the infinite geodesics are horizontal lines under the assumption that the sub-Finsler metric…

We consider a version of Hermitian-Einstein equation but perturbed by a Higgs field with a solution called a Donaldson-Thomas instanton on compact K\"ahler threefolds. The equation could be thought of as a generalization of the Hitchin…