arXiv research

Study shows isolated singularities in maps to K3 surfaces.

In four-dimensional gauge theory there exists a well-known correspondence between instantons and holomorphic curves, and a similar correspondence exists between certain octonionic instantons and triholomorphic curves. We prove that this latter correspondence stems from the dynamics of various dimensional reductions of …

We consider triholomorphic maps from an almost hyper-Hermitian manifold $\mathcal{M}^{4m}$ into a hyperKähler manifold $\mathcal{N}^{4n}$. This means that $u \in W^{1,2}$ satisfies a quaternionic del-bar equation. We work under the assumption that $u$ is locally strongly approximable in $W^{1,2}$ by smooth maps: then s…

A hyperkähler 4-metric with a triholomorphic SU(2) action gives rise to a family of confocal quadrics in Euclidean 3-space when cast in the canonical form of a hyperkähler 4-metric metric with a triholomorphic circle action. Moreover, at least in the case of geodesics orthogonal to the U(1) fibres, both the covariant S…

We show that a complete simply-connected hyperkaehler 4-manifold with an isometric triholomorphic circle action is obtained from the Gibbons-Hawking ansatz with some suitable harmonic function.

We characterise the actions, by holomorphic isometries on a Kähler manifold with zero first Betti number, of an abelian Lie group of dim\geq 2, for which the moment map is horizontally weakly conformal (with respect to some Euclidean structure on the Lie algebra of the group). Furthermore, we study the hyper-Kähler mom…

We obtain explicitly all solutions of the SU(infinity) Toda field equation with the property that the associated Einstein-Weyl space admits a 2-sphere of divergence-free shear-free geodesic congruences. The solutions depend on an arbitrary holomorphic function and give rise to new hyperKahler and selfdual Einstein metr…

We consider a hyperkähler $8$-manifold admitting either a $U(1) \times \mathbb{R}$, or a $U(1) \times U(1)$ action, where the first factor preserves $g$ and $I$, and acts on $ω_2+iω_3$ by multiplying it by itself, while the second factor preserves $g$ and acts triholomorphically. Such data can be reduced to a single fu…

We study relations between quaternionic Riemannian manifolds admitting different types of symmetries. We show that any hyperKahler manifold admitting hyperKahler potential and triholomorphic action of S^1 can be constructed from another hyperKahler manifold (of lower dimention) with an action of S^1 which fixes one com…

We study the Jones and Tod correspondence between selfdual conformal 4-manifolds with a conformal vector field and abelian monopoles on Einstein-Weyl 3-manifolds, and prove that invariant complex structures correspond to shear-free geodesic congruences. Such congruences exist in abundance and so provide a tool for cons…

The article explores the mapping class group using unicellular maps and provides filtrations.

Constructs a moment map flow for isotropic maps on surfaces.

Deep learning classifies seven types of maps for better access.

The paper constructs biharmonic maps between spheres using polynomial maps.

Both bi-harmonic map and $f$-harmonic map have nice physical motivation and applications. In this paper, by combination of these two harmonic maps, we introduce and study $f$-bi-harmonic maps as the critical points of the $f$-bi-energy functional $\frac{1}{2}\int_M f|τ(φ)|^2dv_{g}$. This class of maps generalizes both …

Generic pseudo-Anosov mapping classes in mapping class groups.

Paper constructs maps for sutured monopole Floer homology.

The paper generalizes Reeb spaces for special generic maps and lifts smooth functions.

Research explores real algebraic realization of round fold maps of codimension -1.

Study shows pure mapping classes can generate pseudo-Anosov mapping classes with certain conditions.

The paper derives Liouville theorems for various generalized maps on Riemannian manifolds.

Study of liftable mapping class group for superelliptic covers.

This paper shows semi-equivelar toroidal maps are vertex-transitive covers.

Paper defines and studies Clairaut warped product Riemannian maps.

Study shows no boundary maps for certain groups.

The paper explores unique continuation properties for polyharmonic maps between Riemannian manifolds.

This paper constructs real algebraic maps that are topologically special generic maps.

Derives stress-energy tensor for polyharmonic maps.

The paper constructs gluing maps for harmonic maps between Riemannian manifolds.

Characterizes a general range decreasing group homomorphism.

The paper examines $HM$-tensional and $HS$-tensional maps between Riemannian manifolds.

The paper proves a Liouville theorem for specific harmonic maps with free boundary.

Dirac-harmonic maps are uncoupled under certain conditions.

Paper preserves properties of mappings through generic mappings.

We introduce slant Riemannian maps from Riemannian manifolds to almost Hermitian manifolds as a generalization of slant immersions, invariant Riemannian maps and anti-invariant Riemannian maps. We give examples, obtain characterizations and investigate the harmonicity of such maps. We also obtain necessary and sufficie…

The paper studies maps from pseudo-Hermitian to Kähler manifolds, proving harmonic map properties.

The article explores constructing biharmonic and conformal biharmonic maps to spheres.

Analyzes harmonic and biharmonic maps from gradient Ricci solitons.

Characterizes conformal Gauss maps into spheres.

New theorem proves convergence of various discrete conformal structures to conformal maps.

Method computes harmonic and conformal maps from point clouds.

In this paper, we show that one can interrelate pluriharmonic maps with para-pluriharmonic maps by means of the loop group method. As an appendix, we give examples for the interrelation between pluriharmonic maps and para-pluriharmonic maps. Moreover, we investigate the relation among CMC-surfaces by use of such maps.

Harmonic map flow preserves almost-holomorphic maps without singularities.

The study classifies equivariant biharmonic maps and proves stability results for certain maps.

This paper classifies semi-equivelar maps on a special surface.

The study identifies 11 types of semi-equivelar maps on the torus, with some being vertex-transitive.

Study isotropic Riemannian maps and helices along them.

Study on harmonic maps between cones, linking degrees to graph Laplacian eigenvalues.