Related papers: Real analytic curves of almost complex structures

In this paper, we build a compactification by a strictly pseudoconvex CR structure for complete and non-compact K\"ahler manifolds whose curvature tensor is asymptotic to that of the complex hyperbolic space.

The paper investigates the (non)existence of compact quotients, by a discrete subgroup, of the homogeneous almost-complex strongly-pseudoconvex manifolds disconvered and classified by Gaussier-Sukhov and K.-H. Lee.

The space of orientation-compatible almost complex structures on the six-dimensional sphere naturally contains a copy of seven-dimensional real projective space. We show that the inclusion induces an isomorphism on fundamental groups and…

Let M be a compact, orientable, mean convex 3-manifold with boundary. We show that the set of all simple closed curves in the boundary of M which bound unique area minimizing disks in M is dense in the space of simple closed curves in the…

An almost complex torus manifold is a $2n$-dimensional compact connected almost complex manifold equipped with an effective action of a real $n$-dimensional torus $T^n \simeq (S^1)^n$ that has fixed points. For an almost complex torus…

Let M be a closed (n-1)-connected 2n-dimensional smooth manifold with n > 2. In terms of the system of invariants for such manifolds introduced by Wall, we obtain necessary and sufficient conditions for M to admit an almost complex…

Let M be an almost complex manifold equipped with a Hermitian form such that its de Rham differential has Hodge type (3,0)+(0,3), for example a nearly Kahler manifold. We prove that any connected component of the moduli space of…

The space of the structure (0,3)-tensors of the covariant derivatives of the structure endomorphism and the metric on almost contact B-metric manifolds is considered. A known decomposition of this space in orthogonal and invariant subspaces…

Proof of existence of a complex structure on the six-sphere, followed by an explicit computation of its underlying integrable almost complex tensor by the aid of inner automorphisms of the octonions, is exhibited. Both are elementary and…

The Lichnerowicz conjecture asserts that all harmonic manifolds are either flat or locally symmetric spaces of rank 1. This conjecture has been proved by Z.I. Szabo for harmonic manifolds with compact universal cover. E. Damek and F. Ricci…

The Newlander-Nirenberg theorem says that a necessary and sufficient condition for the complex coordinates associated with a given almost complex structure tensor $I_M{}^N$ to exist is the vanishing of the Nijenhuis tensor ${\cal…

A $p$-K\"ahler structure on a complex manifold of complex dimension $n$ is given by a $d$-closed transverse real $(p,p)$-form. In the paper we study the existence of $p$-K\"ahler structures on compact quotients of simply connected Lie…

In the present work we consider an almost complex manifold with Norden metric (i.e. a metric with respect to which the almost complex structure is an antiisometry). On such a manifold we study a linear connection preserving the almost…

A field of endomorphisms $R$ is called a Nijenhuis operator if its Nijenhuis torsion vanishes. In this work we study a specific kind of singular points of $R$ called points of scalar type. We show that the tangent space at such points…

We prove that for almost complex structures of H\"older class at least 1/2, any J-holomorphic disc, that is constant on some non empty open set, is constant. This is in striking contrast with well known, trivial, non-uniqueness results. We…

In this paper we consider the existence and regularity of weakly polyharmonic almost complex structures on a compact almost Hermitian manifold $M^{2m}$. Such objects satisfy the elliptic system weakly $[J, \Delta^m J]=0$. We prove a very…

We prove that N\'eron models of jacobians of generically-smooth nodal curves over bases of arbitrary dimension are quasi-compact (hence of finite type) whenever they exist. We give a simple application to the orders of torsion subgroups of…

We use an isomorphism between the space of valence two Killing tensors on an n-dimensional constant sectional curvature manifold and the irreducible GL(n+1)-representation space of algebraic curvature tensors in order to translate the…

In this work we study the existence of invariant almost complex structures on real flag manifolds associated to split real forms of complex simple Lie algebras. We show that, contrary to the complex case where the invariant almost complex…

An operator $I$ on a real Lie algebra $A$ is called a complex structure operator if $I^2=-Id$ and the $\sqrt{-1}$-eigenspace $A^{1,0}$ is a Lie subalgebra in the complexification of $A$. A hypercomplex structure on a Lie algebra $A$ is a…