arXiv research

Geometric equation defines canonical metrics on vector bundle families.

The paper constructs a family of SKT metrics on the exceptional Lie group G2.

The study constructs families of nilpotent Lie groups with geodesic orbit metrics.

In his work on the Farrell-Jones Conjecture, Arthur Bartels introduced the concept of a "finitely $\mathcal{F}$-amenable" group action, where $\mathcal{F}$ is a family of subgroups. We show how a finitely $\mathcal{F}$-amenable action of a countable group $G$ on a compact metric space, where the asymptotic dimensions o…

Develops a new family of signature-changing models on metric manifolds.

In this article we introduce a family of elastic metrics on the space of parametrized surfaces in 3D space using a corresponding family of metrics on the space of vector valued one-forms. We provide a numerical framework for the computation of geodesics with respect to these metrics. The family of metrics is invariant …

Manifolds with fibered hyperbolic cusp metrics include hyperbolic manifolds with cusps and locally symmetric spaces of Q-rank one. We extend Vaillant's treatment of Dirac-type operators associated to these metrics by weaking the hypotheses on the boundary families through the use of Fredholm perturbations as in the fam…

We show that the one-loop quantum deformation of the universal hypermultiplet provides a family of complete $1/4$-pinched negatively curved quaternionic Kähler (i.e. half conformally flat Einstein) metrics $g^c$, $c\ge 0$, on $\mathbb R^4$. The metric $g^0$ is the complex hyperbolic metric whereas the family $(g^c)_{c>…

Using Hawking Taub-NUT metric $g_a$ on $\mathbf{R}^4$, where $a$ is a positive real number and finding a 4-parameter family of Killing vector fields of $(\mathbf{R}^4,g_a)$, we construct a 5-parameter family of Einstein Randers metrics with non-constant flag curvature.

Study finds infinite families of Sasaki-Einstein metrics on spheres.

Optimal family of Calabi-Yau cone metrics found for toric Kähler cones.

New examples of degenerating metrics on R^4 found.

This work shows all conformally Kähler, Ricci-flat toric metrics on non-compact surfaces are known families.

Smooth families of biholomorphisms between strongly pseudoconvex domains are shown to be smooth.

The twistor space of self-dual positive Einstein manifolds naturally admits two 1-parameter families of Riemannian metrics, one is the family of canonical deformation metrics and the other is the family introduced by B. Chow and D. Yang in 1989. The purpose of this paper is to compare these two families. In particular …

The paper constructs metrics on spheres with families of minimal hypersurfaces.

On a 4-dimensional compact symplectic manifold, we consider a smooth family of compatible almost-complex structures such that at time zero the induced metric is Hermite-Einstein almost-Kähler metric with zero or negative Hermitian scalar curvature. We prove, under certain hypothesis, the existence of a smooth family of…

The paper explores families of Finsler metrics and their properties.

This paper begins to study the limiting behavior of a family of Hermitian Yang-Mills (HYM for brevity) metrics on a class of rank two slope stable vector bundles over a product of two elliptic curves with Kähler metrics $ω_ε$ when $ε\to 0$. Here $ω_ε$ are flat and have areas $ε$ and $ε^{-1}$ on the two elliptic curves …

We address the question: how large is the family of complete metrics with nonnegative sectional curvature on S^2xR^3? We classify the connection metrics, and give several examples of non-connection metrics. We provide evidence that the family is small by proving some rigidity results for metrics more general than conne…

Polyhomogeneous expansions for Calabi-Yau metrics near singularities.

Positive scalar curvature metrics on cobordisms yield only reducible Seiberg-Witten solutions.

Let X be a G-space such that the orbit space X/G is metrizable. Suppose a family of slices is given at each point of X. We study a construction which associates, under some conditions on the family of slices, with any metric on X/G an invariant metric on X. We show also that a family of slices with the required propert…

Formula derived for volume entropy of certain metrics on Euclidean space.

Study examines heart and football-shaped metrics, verifying geometric structure.

Constructs Einstein metrics on manifolds with specific orbits.

Researchers construct explicit bundles for ALF metrics, revealing rational patching matrices for gravitational instantons.

We construct a family of Calabi-Yau metrics on $\C^3$ with properties analogous to the Taub-NUT metric on $\C^2$, and construct a family of Calabi-Yau 3-fold metric models on the positive and negative vertices of SYZ fibrations with properties analogous to the Ooguri-Vafa metric.

The paper solves a geometric problem related to K3 surfaces and complex-hyperkähler metrics.

We obtain new families of (1,2)-symplectic invariant metrics on the full complex flag manifolds F(n). For n > 4, we characterize n-3 different n-dimensional families of (1,2)-symplectic invariant metrics on F(n). Any of these families corresponds to a different class of non-integrable invariant almost complex structure…

New maximal families of compatible Poisson structures derived from geodesically equivalent metrics.

Using Takahashi theorem we propose an approach to extend known families of minimal tori in spheres. As an example, the well-known two-parametric family of Lawson tau-surfaces including tori and Klein bottles is extended to a three-parametric family of tori and Klein bottles minimally immersed in spheres. Extremal spect…

Study describes ALF instantons with conical singularities.

We construct quasi-Einstein metrics on some hypersurface families. The hypersurfaces are circle bundles over the product of Fano, Kähler-Einstein manifolds. The quasi-Einstein metrics are related to various gradient Kähler-Ricci solitons constructed by Dancer and Wang and some Hermitian, non-Kähler, Einstein metrics co…

We construct continuous families of Riemannian metrics on certain simply connected manifolds with the property that the resulting Riemannian manifolds are pairwise isospectral for the Laplace operator acting on functions. These are the first examples of simply connected Riemannian manifolds without boundary which are i…

Study degenerations of Kähler-Einstein metrics on surfaces.

A 6-parametric family of 6--dimensional quasi-Kähler manifolds with Norden metric is constructed on a Lie group. This family is characterized geometrically.

New separation concepts for Anosov representations help bound Thurston asymmetric metric.

Analyzes Kähler-Einstein metrics on families of Fano varieties.

Study compares metrics from negative curvature and quasi-Fuchsian representations.

A 4n-parametric family of 4n-dimensional quasi-Kaehler manifolds with Killing Norden metric is constructed on a Lie group. This family is characterized geometrically.

An efficient algorithm for Riemannian logarithm on Stiefel manifold family.

The paper finds new $\mathrm{Spin}(7)$ metrics with specific orbits.

New metrics improve landing algorithms for orthogonality constraints.

Locally, isoperimetric problems on Riemannian surfaces are sub-Riemannian problems in dimension 3. The particular case of Dido problems corresponds to a class of singular contact sub-Riemannian metrics : metrics which have the charateristic vertor field as symmetry. We give a classification of the generic conjugate loc…

We construct continuous families of scattering manifolds with the same scattering phase. The manifolds are compactly supported metric perturbations of Euclidean $\mathbf{R}^{n}$ for $n\geq8$. The metric perturbation may have arbitrarily small support.

New formulas for Riemannian gradient and Hessian on manifold metrics.

Researchers prove spectral uniqueness of complex/quaternionic structures on manifolds.