Related papers: Biharmonic maps from tori into a 2-sphere
This paper studies conformal biharmonic immersions. We first study the transformations of Jacobi operator and the bitension field under conformal change of metrics. We then obtain an invariant equation for a conformal biharmonic immersion…
This note reviews some of the recent work on biharmonic conformal maps (see \cite{OC}, Chapter 11, for a detailed survey). It will be focused on biharmonic conformal immersions and biharmonic conformal maps between manifolds of the same…
A neighborhood homotopy is an equivalence relation on spatial graphs which is generated by crossing changes on the same component and neighborhood equivalence. We give a complete classification of all 2-component spatial graphs up to…
We present an explicit description of all harmonic maps of finite uniton number from a Riemann surface into a complex Grassmannian. Namely, starting from a constant map $Q$ and a collection of meromorphic functions and their derivatives, we…
In 1936 H. Lewy showed that the Jacobian determinant of a harmonic homeomorphism between planar domains does not vanish and thus the map is a diffeomorphism. This built on the earlier existence results of Rad\'o and Kneser. R. Shoen and…
We show a non-existence result for some class of equivariant maps between sphere bundles over tori. The notion of equivariant KO-degree is used in the proof. As an application to Seiberg-Witten theory, for a connected closed oriented spin…
This article studies the harmonicity of vector fields on Riemannian manifolds, viewed as maps into the tangent bundle equipped with a family of Riemannian metrics. Geometric and topological rigidity conditions are obtained, especially for…
A hypersurface is said to be totally biharmonic if all its geodesics are biharmonic curves in the ambient space. We prove that a totally biharmonic hypersurface into a space form is an isoparametric biharmonic hypersurface, which allows us…
Harmonic maps are important in generating parameterizations for various domains, particularly in two and three dimensions. General extensions of two-dimensional harmonic parameterizations for volumetric parameterizations are known to fail…
The distributive property can be studied through bilinear maps and various morphisms between these maps. The adjoint-morphisms between bilinear maps establish a complete abelian category with projectives and admits a duality. Thus the…
In this paper, we mainly derive monotonicity formula of generalized map using conservation law, including $\phi$-$F$ harmonic map coupled with $\phi$-$F$ symphonic map with $m$ form and potential from metric measure space, $ p $ harmonic…
In this article we study polyharmonic curves of constant curvature where we mostly focus on the case of curves on the sphere. We classify polyharmonic curves of constant curvature in three-dimensional space forms and derive an explicit…
We estimate the dimensions of the spaces of holomorphic sections of certain line bundles to give improved lower bounds on the index of complex isotropic harmonic maps to complex projective space from the sphere and torus, and in some cases…
A one parameter set of noncommutative complex algebras is given. These may be considered deformation quantisation algebras. The commutative limit of these algebras correspond to the algebra of polynomial functions over a manifold or…
We initiate and develop the theory of complex harmonic maps to holomorphic Riemannian symmetric spaces, which we make use of to study complex analytic aspects of higher Teichm\"uller theory, with a focus on rank $2$ Hitchin components.…
We show that the notions of homotopy epimorphism and homological epimorphism in the category of differential graded algebras are equivalent. As an application we obtain a characterization of acyclic maps of topological spaces in terms of…
In this article, we prove energy quantization for approximate (intrinsic and extrinsic) biharmonic maps into spheres where the approximate map is in $L \log L$. Moreover, we demonstrate that if the $L\log L$ norm of the approximate maps…
We determine all local smooth or formal CR maps from the unit sphere $\mathbb{S}^3\subset \mathbb{C}^2$ into the tube $\mathcal{T}:= \mathcal{C} \times i\mathbb{R}^3 \subset \mathbb{C}^3$ over the future light cone $\mathcal{C}:=…
Semi-Equivelar maps are generalizations of Archimedean solids to the surfaces other than 2-sphere. There are eight semi-equivelar maps of types $\{3^{3},4^{2}\}$, $\{3^{2},4,3,4\}$, $\{6,3,6,3\}$, $\{3^{4},6\}$, $\{4,8^{2}\}$,…
We derive various classification results for polyharmonic helices, which are polyharmonic curves whose geodesic curvatures are all constant, in space forms. We obtain a complete classification of triharmonic helices in spheres of arbitrary…