arXiv research

In this paper, we introduce a study of prolongations of homogeneous vector bundles. We give an alternative approach for the prolongation. For a given homogeneous vector bundle E, we obtain a new homogeneous vector bundle. The homogeneous structure and its corresponding representation are derived. The prolongation of in…

We introduce the concept of a graded bundle which is a natural generalization of the concept of a vector bundle and whose standard examples are higher tangent bundles T^nQ playing a fundamental role in higher order Lagrangian formalisms. Graded bundles are graded manifolds in the sense that we can choose an atlas whose…

For Fano homogeneous toric bundles, we obtain a formula of the greatest lower bound on Ricci curvature. We also give a criteria for the ampleness of a kind of line bundles over general homogeneous toric bundles.

Proves Yau-Tian-Donaldson conjecture for toric manifolds and bundles.

This article deals with fat bundles. Berard-Bergery classified all homogeneous bundles of that type. We ask a question of a possibility to generalize his description in the case of arbitrary G-structures over homogeneous spaces. We obtain necessary conditions for the existence of such bundles. These conditions yield a …

Einstein metrics on homogeneous torus bundles

In this paper, we provide a systematic and constructive description of Vaisman structures on certain principal elliptic bundles over complex flag manifolds. From this description we explicitly classify homogeneous l.c.K. structures on compact homogeneous Hermitian manifolds using elements of representation theory of co…

Global Pestov identity proved on frame bundle and related fibrations.

Develops global pseudo-differential calculus on homogeneous vector bundles.

The paper introduces a new concept of infinitesimal homogeneity for connections on bundles and applies it to prove known theorems and derive new results.

The paper studies weak singular Hermite-Einstein structures on homogeneous vector bundles.

It is proved that an homogeneous toric bundles over a flag manifold G^\C/P admits a Kaehler-Ricci solitonic metric if and only if it is Fano. In particular, an homogeneous toric bundle of this kind is Kaehler-Einstein if and only if it is Fano and its Futaki invariant vanishes identically.

We provide new examples of manifolds which admit a Riemannian metric with sectional curvature nonnegative, and strictly positive at one point. Our examples include the unit tangent bundles of $CP^n$, $HP^n$ and $CaP^2$, and a family of lens space bundles over $CP^n$. All new examples are consequences of a general suffi…

We study a generalized Abreu Equation in $n$-dimensional polytopes and prove some differential inequalities for homogeneous toric bundles.

Abstract not provided enough details, focusing on vector bundles and orbits.

GCNNs on homogeneous spaces use vector bundles and Hilbert spaces.

Method constructs 2-bundles over homogeneous spaces.

We consider cohomogeneity one homogeneous disk bundles and adress the question when these admit a nonnegatively curved invariant metric with normal collar, i.e., such that near the boundary the metric is the product of an interval and a normal homogeneous space. If such a bundle is not (the quotient of) a trivial bundl…

Study shows no hyperkähler fourfolds in specified conditions.

Compact quotients of homogeneous spaces are studied, leading to new findings about sphere bundles.

Classifies Higgs and co-Higgs bundles on symmetric spaces.

We complete our recent classification of compact inner symmetric spaces with weakly complex tangent bundle by filling up a case which was left open, and extend this classification to the larger category of compact homogeneous spaces with positive Euler characteristic. We show that a simply connected compact equal rank …

New product manifolds can have non-negative curvature.

We prove the stability of the Gieseker point of an irreducible homogeneous bundle over a rational homogeneous space. As an application we get a sharp upper estimate for the first eigenvalue of the Laplacian of an arbitrary Kaehler metric on a compact Hermitian symmetric spaces of ABCD--type.

Geometric study of thermodynamics using cotangent bundles.

A simple algebraic characterization of the Fano manifolds in the class of homogeneous toric bundles over a flag manifold $G^C/P$ is provided in terms of symplectic data.

This is the first of a sequence of two papers. Here, a simple algebraic characterization of the Fano manifolds in the class of homogeneous toric bundles over a flag manifold G^C/P is provided in terms of symplectic data. The result of this paper is used in the second paper, where it is proved that an homogeneous toric …

The paper introduces controllable principal connections and estimates distances between bundles and spaces.

In this paper we study holomorphic vector bundles with singular Hermitian metrics whose curvature are Hermitian matrix currents. We obtain an extension theorem for holomorphic jet sections of nef holomorphic vector bundle on compact Kähler manifolds. Using it we prove that Fano manifolds with strong Griffiths nef tange…

We show the vanishing of the log-term in the Fefferman expansion of the Bergman kernel of the disk bundle over a compact simply-connected homogeneous Kaehler--Einstein manifold of classical type.

In this paper, we study the generalized Abreu equation on a Delzant ploytope $Δ\subset \mathbb{R}^2$ and prove the existence of the constant scalar metrics of homogeneous toric bundles under the assumption of an appropriate stability.

Let $ξ=(G\times_{K} \mathcal{G} / \mathcal{K}, ρ_ξ, \emph{G} / \emph{K},\mathcal{G} / \mathcal{K})$ be the associated bundle and $τ_{G/K}=(T_{G/K},π_{G/K},G/K, \textrm{R}^{m})$ be the tangent bundle of special examples of odd dimension solvable Lie groups equipped with left invariant Riemannian metric. In this paper we…

Let $M$ be a differentiable manifold and $K$ a Lie group. A locally homogeneous triple with structure group $K$ on $M$ is a triple $(g, P\stackrel{p}{\to} M,A)$, where $p:P\to M$ is a principal $K$-bundle on $M$, $g$ is Riemannian metric on $M$, and $A$ is connection on $P$ such that the following locally homogeneity c…

Unified method to compute Laplace spectra on homogeneous principal bundles.

The paper studies graded manifolds and their functorial relationship.

New dHYM connections found on complex vector bundles.

Study on higher order Levi forms on homogeneous CR manifolds, improving previous results.

For homogeneous simply connected Hodge manifolds it is proved that the set of coherent vectors orthogonal to a given one is the divisor responsible for the homogeneous holomorphic line bundle of the coherent vectors. In particular, for naturally reductive spaces, the divisor is the cut locus.

Let $G$ be the identity component of the isometry group for an arbitrary curved two-point homogeneous space $M$. We consider algebras of $G$-invariant differential operators on bundles of unit spheres over $M$. The generators of this algebra and the corresponding relations for them are found. The connection of these ge…

We determine the holonomy of generalized Killing spinor covariant derivatives of the form $D= \nabla + Ω$ on pseudo-Riemannian reductive homogeneous spaces in a purely algebraic and algorithmic way, where $Ω: TM \rightarrow Λ^*(TM)$ is a left-invariant homomorphism. This is essentially an application of the theory of i…

Let G be a Lie supergroup and H a closed subsupergroup. We study the unimodularity of the homogeneous supermanifold G/H, i.e. the existence of G-invariant sections of its Berezinian line bundle. To that end, we express this line bundle as a G-equivariant associated bundle of the principal H-bundle G over G/H. We also s…

A new algebraic structure emerges from reductive homogeneous spaces.

New methods for constructing submersions between different types of spaces.

We present an approach to Jacobi and contact geometry that makes many facts, presented in the literature in an overcomplicated way, much more natural and clear. The key concepts are Kirillov manifolds and linear Kirillov structures, i.e., homogeneous Poisson manifolds and, respectively, homogeneous linear Poisson manif…

Researchers discover all affinely homogeneous models for surfaces in 4D space.

Classifies 6D homogeneous spaces with holomorphically trivial canonical bundle.

A new method simplifies contact Hamiltonian mechanics.

Study Nijenhuis operators on Banach homogeneous spaces, extending previous work.