arXiv research

Study on unique solutions to one-phase free boundary problems.

We use spectral embeddings to give upper bounds on the spectral function of the Laplace--Beltrami operator on homogeneous spaces in terms of the volume growth of balls. In the case of compact manifolds, our bounds extend the 1980 lower bound of Peter Li for the smallest positive eigenvalue to all eigenvalues. We also i…

The paper generalizes equivariant neural networks on homogeneous spaces to the non-linear setting.

Ricci flow preserves positive sectional curvature on homogeneous spheres

Study invariant Poisson structures on homogeneous manifolds, algebraically and geometrically.

Study BGG operators on homogeneous conformal geometries.

We consider canonical fibrations and algebraic geometric structures on homogeneous CR manifolds, in connection with the notion of CR algebra. We give applications to the classifications of left invariant CR structures on semisimple Lie groups and of CR-symmetric structures on complete flag varieties.

Steerable neural ODEs on homogeneous spaces for equivariant feature dynamics.

Geodesic orbit metrics proven on specific homogeneous spaces.

Study first BGG operators on homogeneous geometries.

In this paper we consider invariant Matsumoto metrics which are induced by invariant Riemannian metrics and invariant vector fields on homogeneous spaces then we give the flag curvature formula of them. Also we study the special cases of naturally reductive spaces and bi-invariant metrics. We end the article by giving …

The study preserves Ricci curvature positivity on homogeneous spaces under the normalized Ricci flow.

The concept of soliton, in its most general version, allows us to find canonical or distinguished elements on any set provided with an equivalence relation and an `optimal' tangent direction at each point. We study in this paper solitons on homogeneous spaces, which have consolidated its role as a quite useful tool to …

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

Develops global pseudo-differential calculus on homogeneous vector bundles.

The paper classifies tensors on specific Lorentzian metrics.

In this paper, we consider half-flat $SU(3)$-structures and the subclasses of coupled and double structures. In the general case we show that the intrinsic torsion form $w_1^-$ is constant in each of the two subclasses. We then consider the problem of finding half-flat structures inducing Einstein metrics on homogeneou…

Two metrics on a manifold are geodesically equivalent if sets of their unparameterized geodesics coincide. In this paper we show that if two left $G$-invariant metrics of arbitrary signature on homogenous space $G/H$ are geodesically equivalent, they are affinely equivalent, i.e. they have the same Levi-Civita connecti…

The paper studies Einstein metrics on homogeneous supermanifolds.

Paper proves every homogeneous Landsberg surface is either Riemannian or locally Minkowskian.

Many extensions of General Relativity are based on considering metric and affine structures as independent properties of spacetime. This leads to the possibility of introducing torsion as an independent degree of freedom. In this article we examine the effects of torsion on the affine Killing vectors of two-dimensional…

Study Palais-Smale sequences for Ricci curvature on homogeneous spaces.

Einstein metrics on homogeneous torus bundles

Study spectral settings of generalized Laplacians on homogeneous spaces.

We consider Laplacians acting on sections of homogeneous vector bundles over symmetric spaces. By using an integral representation of the heat semi-group we find a formal solution for the heat kernel diagonal that gives a generating function for the whole sequence of heat invariants. We argue that the obtained formal s…

We develop a general approach to study geometric flows on homogeneous spaces. Our main tool will be a dynamical system defined on the variety of Lie algebras called the bracket flow, which coincides with the original geometric flow after a natural change of variables. The advantage of using this method relies on the fa…

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

In this paper we show some results on homogeneous CR manifolds, proved by introducing their associated CR algebras. In particular, we give different notions of nondegeneracy (generalizing the usual notion for the Levi form) which correspond to geometrical properties for the corresponding manifolds. We also give disting…

In this article we review the recent results about the flag curvature of invariant Randers metrics on homogeneous manifolds and by using a counter example we show that the formula which obtained for the flag curvature of these metrics is incorrect. Then we give an explicit formula for the flag curvature of invariant Ra…

Consider a compact Lie group $G$ and a closed Lie subgroup $H<G$. Let $\mathcal M$ be the set of $G$-invariant Riemannian metrics on the homogeneous space $M=G/H$. By studying variational properties of the scalar curvature functional on $\mathcal M$, we obtain an existence theorem for solutions to the prescribed Ricci …

Shape analysis is ubiquitous in problems of pattern and object recognition and has developed considerably in the last decade. The use of shapes is natural in applications where one wants to compare curves independently of their parametrisation. One computationally efficient approach to shape analysis is based on the Sq…

We consider automorphisms of homogeneous parabolic geometries with a fixed point. Parabolic geometries carry the distinguished distributions and we study those automorphisms which enjoy natural actions on the distributions at the fixed points. We describe the sets of such automorphisms on homogeneous parabolic geometri…

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

We find Einstein metrics on homogeneous HKT manifolds.

In the present article we compute the flag curvature of a special type of invariant Kropina metrics on homogeneous spaces.

In the present paper, the flag curvature of invariant Randers metrics on homogeneous spaces and Lie groups is studied. We first give an explicit formula for the flag curvature of invariant Randers metrics arising from invariant Riemannian metrics on homogeneous spaces and, in special case, Lie groups. We then study Ran…

Researchers study metrics with maximal Ricci curvature on homogeneous spaces.

Study shows nontrivial intersections of subgroups on homogeneous spaces.

Study stability of Einstein metrics on homogeneous spaces.

We complete the classification, initiated by the second named author, of homogeneous singular Riemannian foliations of spheres that are lifts of foliations produced from Clifford systems.

We prove complete integrability of the Manakov-type SO(n)-invariant geodesic flows on homogeneous spaces $SO(n)/SO(k_1)\times...\times SO(k_r)$, for any choice of $k_1,...,k_r$, $k_1+...+k_r\le n$. In particular, a new proof of the integrability of a Manakov symmetric rigid body motion around a fixed point is presented…

New integrators for Lagrangian systems on homogeneous spaces derived from nonholonomic mechanics.

Left-invariant Cotton solitons on homogeneous manifolds are determined. Moreover, algebraic Cotton solitons are studied providing examples of non-invariant Cotton solitons, both in the Riemannian and Lorentzian homogeneous settings.

We define naturally Hermite-Lorentz metrics on almost-complex manifolds as special case of pseudo-Riemannian metrics compatible with the almost complex structure. We study their isometry groups.

We study the utility indifference price of a European option in the context of small transaction costs. Considering the general setup allowing consumption and a general utility function at final time T, we obtain an asymptotic expansion of the utility indifference price as a function of the asymptotic expansions of the…

The paper studies Einstein metrics on specific manifolds and their rigidity properties.

Classified spaces in low dimensions.

The paper studies foliations on homogeneous spaces and identifies specific foliations.