相关论文: A survey on locally Homogeneous almost-Hermitian s…

We examine the $L^2$-topology of the gauge orbits over a closed Riemann surface. We prove a subtle local slice theorem based on the div-curl Lemma of harmonic analysis, and deduce local pathwise connectedness and local uniform…

We explicitly construct a symplectomorphism that relates magnetic twists to the invariant hyperk\"ahler structure of the tangent bundle of a Hermitian symmetric space. This symplectomorphism reveals foliations by (pseudo-) holomorphic…

Motivated by Felix Klein's notion that geometry is governed by its group of symmetry transformations, Charles Ehresmann initiated the study of geometric structures on topological spaces locally modeled on a homogeneous space of a Lie group.…

We study equivariant embeddings with small boundary of a given homogeneous space $G/H$, where $G$ is a connected, linear algebraic group with trivial Picard group and only trivial characters, and $H \subset G$ is an extension of a connected…

In this paper, we study the existence of various harmonic maps from Hermitian manifolds to Kaehler, Hermitian and Riemannian manifolds respectively. By using refined Bochner formulas on Hermitian (possibly non-Kaehler) manifolds, we derive…

We show that the de Rham complex of any almost Hermitian manifold carries a natural commutative $BV_\infty$-algebra structure satisfying the degeneration property. In the almost K\"ahler case, this recovers Koszul's BV-algebra, defined for…

We study curvature properties of four-dimensional almost Hermitian manifolds with vanishing Bochner curvature tensor as defined by Tricerri and Vanhecke. We give local structure theorems for such Kaehler manifolds, and find out several…

We explore complex Riemannian geometry and Hermitian metrics on complex algebraic varieties and analytic spaces, respectively. In particular, we introduce Hermitian metrics on holomorphic Lie algebroids and examine the associated…

Ambrose and Singer characterized connected, simply-connected and complete homogeneous Riemannian manifolds as Riemannian manifolds admitting a metric connection such that its curvature and torsion are parallel. The aim of this paper is to…

Let M be an almost complex manifold equipped with a Hermitian form such that its de Rham differential has Hodge type (3,0)+(0,3), for example a nearly Kahler manifold. We prove that any connected component of the moduli space of…

A tractable definition of the homogeneous nearly K\"ahler structure on $\mathbb{C}P^3$ is given via the Hopf fibration, facilitating explicit computations and analysis. The description extends to all homogeneous metrics on $\mathbb{C}P^3$,…

This work deals with relations between a bounded cohomological invariant and the geometry of Hermitian symmetric spaces of noncompact type. The invariant, obtained from the K\"ahler class, is used to define and characterize a special class…

For g a split semisimple Lie algebra over a field of characteristic 0, we link locally trivial principal homogeneous spaces over Spec(R) to the question of conjugacy of maximal abelian diagonalizable subalgebras of g(R).

We study index theory on homogeneous spaces associated to an almost connected Lie group in terms of the topological aspect and the analytic aspect. On the topological aspect, we obtain a topological formula as a result of the Riemann-Roch…

Given a non compact semisimple Lie group $G$ we describe all homogeneous spaces $G/L$ carrying an invariant almost K\"ahler structure $(\omega,J)$. When $L$ is abelian and $G$ is of classical type, we classify all such spaces which are…

In this paper, we investigate equigeodesics on a compact homogeneous space $M=G/H.$ We introduce a formula for the identification of equigeodesic vectors only relying on the isotropy representation of $M$ and the Lie structure of the Lie…

We study the space of pseudo-holomorphic spheres in compact symplectic manifolds with convex boundary. We show that the theory of Gromov-Witten invariants can be extended to the class of semi-positive manifolds with convex boundary. This…

In this paper we study sectional curvature of invariant hyper-Hermitian metrics on simply connected 4-dimensional real Lie groups admitting invariant hypercomplex structure. We give the Levi-Civita connections and explicit formulas for…

We explore the relationship between approximate symmetries of a gapped Hamiltonian and the structure of its ground space. We start by showing that approximate symmetry operators---unitary operators whose commutators with the Hamiltonian…

In this paper, we study the existence of constant holomorphic d-scalar curvature and the prescribing holomorphic d-scalar curvature problem on closed, connected almost Hermitian manifolds of dimension $n\geq6$. In addition, we obtain an…