Related papers: Polyharmonic hypersurfaces into complex space form…
In this note we improve a gap result concerning the range of the mean curvature of complete $CMC$ proper-biharmonic hypersurfaces in unit Euclidean spheres.
Simplicial arrangements are classical objects in discrete geometry. Their classification remains an open problem but there is a list conjectured to be complete at least for rank three. A further important class in the theory of hyperplane…
In this paper, we study biconservative hypersurfaces of index 2 in $\mathbb E^{5}_{2}$. We give the complete classification of biconservative hypersurfaces with diagonalizable shape operator at exactly three distinct principal curvatures.…
Let $\mathbb{R}$ be the field of real numbers. We consider the problem of computing the real isolated points of a real algebraic set in $\mathbb{R}^n$ given as the vanishing set of a polynomial system. This problem plays an important role…
We construct biharmonic real hypersurfaces and Lagrangian submanifolds of Clifford torus type in $CP^n$ via the Hopf fibration; and get new examples of biharmonic submanifolds in $S^{2n+1}$ as byproducts .
We study f-biharmonic and bi-f-harmonic submanifolds in both generalized complex and Sasakian space forms. We prove necessary and sufficient condition for f-biharmonicity and bi-f-harmonicity in the general case and many particular cases.…
We consider the class univalent log-harmonic mappings on the unit disk. Firstly, we obtain necessary and sufficient conditions for a complex-valued continuous function to be starlike or convex in the unit disk. Then we present a general…
In this paper, we prove three related results; (1) Extension of our result in [10] to all generic hypersurfaces. More precisely, the normal sheaf of a generic rational map $c_0$ to a generic hypersurface $X_0$ of $\mathbf P^n, n\geq 4$ has…
We give some general results on proper-biharmonic submanifolds of a complex space form and, in particular, of the complex projective space. These results are mainly concerned with submanifolds with constant mean curvature or parallel mean…
We prove geometric and cohomological stabilization results for the universal smooth degree $d$ hypersurface section of a fixed smooth projective variety as $d$ goes to infinity. We show that relative configuration spaces of the universal…
In this paper, we obtain coefficient criteria for a normalized harmonic function defined in the unit disk to be close-to-convex and fully starlike, respectively. Using these coefficient conditions, we present different classes of harmonic…
We construct a finitely dimensional invariant manifold of holomorphic discs attached to a certain class of smooth pseudconvex hypersurfaces of finite type in $\C^2$, generalizing the notion of stationary discs. The discs we construct are…
We study the class $HQ(\mathbb{D})$, the set of harmonic quasiconformal automorphisms of the unit disk $\mathbb{D}$ in the complex plane, endowed with the topology of uniform convergence. Several important topological properties of this…
In general, the product of harmonic forms is not harmonic. We study the top exterior power of harmonic two-forms on compact Kaehler manifolds. Often, it is not harmonic. This phenomenon is related to the geometry of the manifold and to the…
A survey of some results and open questions related to the following algebraic invariants of compact complex manifolds, that can be obtained from differential forms: cohomology groups, Chern classes, rational homotopy groups, and higher…
A new conformally invariant energy for four-dimensional hypersurfaces is devised. It renders possible the study of a large class of curvature energies, and we show that their critical points are smooth. As corollaries, we obtain the…
We give a necessary and sufficient condition for the existence of nondegenerate holomorphic mappings between pseudoellipsoidal real hypersurfaces, and provide an explicit parametrization for the collection of all such mappings (in the…
In this paper, we study biconservative hypersurfaces in $\mathbb S^{n}$ and $\mathbb H^{n}$. Further, we obtain complete explicit classification of biconservative hypersurfaces in $4$-dimensional Riemannian space form with exactly three…
On non-K\"ahler manifolds the notion of harmonic maps is modified to that of Hermitian harmonic maps in order to be compatible with the complex structure. The resulting semilinear elliptic system is {\it not} in divergence form. The case of…
In this paper, we extend the definition of p-harmonic and p-biharmonic maps between Riemannian manifolds. We present some new properties for the generalized stable p-harmonic maps.