Related papers: Hermitian Harmonic maps and non-degenerate curvatu…

We present some formulae related to the Chern-Ricci curvatures and scalar curvatures of special Hermitian metrics. We prove that a compact locally conformal K\"{a}hler manifold with constant nonpositive holomorphic sectional curvature is…

We prove several K\"ahlerness criteria for compact Hermitian surfaces under semi-definiteness assumptions on natural Ricci curvatures of the Strominger-Bismut connection. The key tools for proving these results are explicit identities…

In this work we present a general formalism to treat non-Hermitian and noncommutative Hamiltonians. This is done employing the phase-space formalism of quantum mechanics, which allows to write a set of robust maps connecting the Hamitonians…

In this paper we are concerned with harmonic maps and minimal immersions defined on compact Riemannian manifolds and with values in homogenous strongly harmonic manifolds. We show some results on the Morse index by varying these maps along…

Motivated by the recent work of Wu and Yau on the ampleness of canonical line bundle for compact K\"ahler manifolds with negative holomorphic sectional curvature, we introduce a new curvature notion called $\textbf{real bisectional…

We find some integral formulas of Simons and Bochner type and use them to study biharmonic and biconservative submanifolds in space forms. We obtain rigidity results that in the biharmonic case represent partial answers to two well-known…

In this two papers we deal with the relative homotopy Dirichlet problem for p-harmonic maps from compact manifolds with boundary to manifolds of non-positive sectional curvature. Notably, we give a complete solution to the problem in case…

This work proves certain general orbifold compactness results for spaces of Riemannian metrics, generalizing earlier results along these lines for Einstein metrics or metrics with bounded Ricci curvature. This is then applied to prove such…

We construct a new class of biharmonic maps, which are the critical points for the bienergy functional, by deforming conformally the codomain metric of harmonic Riemannian submersions such that they become nonharmonic but biharmonic.

We investigate the geometry of Hermitian manifolds endowed with a compact Lie group action by holomorphic isometries with principal orbits of codimension one. In particular, we focus on a special class of these manifolds constructed by…

We study harmonic maps from a 3-manifold with boundary to $\mathbb{S}^1$ and prove a special case of dihedral rigidity of three dimensional cubes whose dihedral angles are $\pi / 2$. Furthermore we give some applications to mapping torus…

In this paper, we investigate subelliptic harmonic maps with potential from noncompact complete sub-Riemannian manifolds corresponding to totally geodesic Riemannian foliations. Under some suitable conditions, we give the gradient estimates…

In this paper, we derived biharmonic equations for pseudo-Riemannian submanifolds of pseudo-Riemannian manifolds which includes the biharmonic equations for submanifolds of Riemannian manifolds as a special case. As applications, we proved…

In the present paper, we introduce bi-slant submersions from almost Hermitian manifolds onto Riemannian manifolds as a generalization of invariant, anti-invariant, semi-invariant, slant, semi-slant and hemi-slant Riemannian submersions. We…

In this article, we study harmonic symmetries on the compact locally conformally K\"{a}hler manifold $M$ of $dim_{\mathbb{C}}=n$. The space of harmonic symmetries is a subspace of harmonic differential forms which defined by the kernel of a…

We study curvature invariants of a sub-Riemannian manifold (i.e., a manifold with a Riemannian metric on a non-holonomic distribution) related to mutual curvature of several pairwise orthogonal subspaces of the distribution, and prove…

In this paper, we study stability for harmonic foliations on locally conformal K\"ahler manifolds with complex leaves. We also discuss instability for harmonic foliations on compact submanifolds immersed in Euclidean spaces and compact…

We review the relations between compact complex manifolds carrying various types of Hermitian metrics (K\"ahler, balanced or {\it strongly Gauduchon}) and those satisfying the $\partial\bar\partial$-lemma or the degeneration at $E_1$ of the…

We prove local existence of complex-valued harmonic morphisms from any Riemannian homogeneous spaces of positive curvature, except the Berger space Sp(2)/SU(2).

We give a partial account of some problems concerning cohomological invariants and metric properties of complex non-K\"ahler manifolds.