On infinitesimal automorphisms of almost contact metric lattices

In this paper, three-dimensional maximum mobile almost contact manifolds are considered. In a special frame, we have obtained the form of structural objects for the case of constant φ-analytic curvature H = −3 of the first and also second and third classes of the Tanno theorem. The basis vector field of the Lie algebra of infinitesimal automorphisms for each of the considered structures and their commutators are found.     

Transversal infinitesimal automorphisms of harmonic foliations on complete manifolds

Summary In this paper we study infinitesimal automorphisms of finiteL ²-norm for harmonic Riemannian and Kähler foliations admitting a complete bundle-like metric. The results generalize facts established recently in the compact case.1980 Mathematics Subject Classification: Primary 57 R 30, Secondary 58 E 20.Work supported in part by a grant from the National Science Foundation.     

Lelong functional on almost complex manifolds

We establish plurisubharmonicity of the envelope of Lelong functional on almost complex manifolds of real dimension four, thereby we generalize the corresponding result for complex manifolds.     

Extension formulae on almost complex manifolds

We give the extension formulae on almost complex manifolds and give decompositions of the extension formulae.As applications,we study(n,0)-forms,the(n,0)-Dolbeault cohomology group and(n,q)-forms on almost complex manifolds.     

Compatible complex structures on almost quaternionic manifolds

On an almost quaternionic manifold we study the integrability of almost complex structures which are compatible with the almost quaternionic structure . If , we prove that the existence of two compatible complex structures forces to be quaternionic. If , that is is an oriented conformal 4-manifold, we prove a maximum principle for the angle function of two compatible complex structures and deduce an application to anti-self-dual manifolds. By considering the special class of Oproiu connections we prove the existence of a well defined almost complex structure on the twistor space of an almost quaternionic manifold and show that is a complex structure if and only if is quaternionic. This is a natural generalization of the Penrose twistor constructions.

     

The Albanese mapping for compact almost complex manifolds

Partially supported by the Forschungsinstitut für Mathematik at the ETH Zuerich     

Chern numbers of almost complex manifolds

It is shown that any system of numbers that can be realised as the system of Chern numbers of an almost complex manifold of dimension , , can also be realised in this way by a connected almost complex manifold. This answers an old question posed by Hirzebruch.

     

On Hermitian curvature flow on almost complex manifolds

In the present paper we generalize the Hermitian curvature flow introduced and studied in Streets and Tian (2011) [6] to the almost complex case.     

J-pluripolar subsets and currents on almost complex manifolds

We prove that every almost complex submanifold of an almost complex manifold is locally J-pluripolar. This generalizes a result of Rosay for J-holomorphic submanifolds. Our second main result is an almost complex version of El Mir’s theorem for the extension of positive currents across locally complete pluripolar sets. As a consequence, we extend some results proved by Dabbek–Elkhadhra–El Mir and Dinh–Sibony in the standard complex case. We also obtain a version of the well-known results of Federer and Bassanelli for flat and mathbb C{mathbb {C}}-flat currents in the almost complex setting.     

Nonpositively curved almost Hermitian metrics on product of compact almost complex manifolds

In this paper, we give a classification of almost Hermitian metrics with nonpositive holomorphic bisectional curvature on a product of compact almost complex manifolds. This generalizes previous results of Zheng [Ann. of Math.(2), 137(3), 671–673(1993)] and the author [Proc. Amer.Math. Soc., 139(4), 1469–1472(2011)].     

Stably and almost complex structures on bounded flag manifolds

We study the enumeration problem of stably complex structures on bounded flag manifolds arising from omniorientations, and determine those induced by almost complex structures. We also enumerate the stably complex structures on these manifolds which bound, therefore representing zero in the complex cobordism ring .

     

An existence theorem for stationary discs in almost complex manifolds

An existence theorem for stationary discs of strongly pseudo-convex domains in almost complex manifolds is proved. More precisely, it is shown that, for all points of a suitable neighborhood of the boundary and for any vector belonging to certain open subsets of the tangent spaces, there exists a unique stationary disc passing through that point and tangent to the given vector. This result gives a generalization of a theorem of B. Coupet, H. Gaussier and the second author, originally proved only for almost complex structures which are small deformations of an integrable one.     

Some aspects of analysis on almost complex manifolds with boundary

We present some results dealing with the local geometry of almost complex manifolds. We establish mainly the complete hyperbolicity of strictly pseudoconvex domains, the extension of plurisubharmonic functions through generic submanifolds, and the elliptic regularity of some diffeomorphisms of almost complex manifolds with boundary. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 47, Complex Analysis, 2007.     

Almost complex structures on connected sums of almost complex manifolds and complex projective spaces

Archiv der Mathematik - For a smooth curve C in $${{mathbb {P}}}^{r_0}$$ lying on a rational surface scroll, we try to identify those complete and base point free linear series of small degree...     

On almost regular automorphisms

Among other things, we prove that a polycyclic group admitting an automorphism of order two with finitely many fixed elements is abelian-by-finite. An example shows that this result cannot be extended to finitely generated soluble groups.     

Distributions on almost contact manifolds

It is known that any hypersurface in an almost complex space admits an almost contact manifold [11, 14]. In this article we show that a hyperplane in an almost contact manifold has an almost complex structure. Along with this result, we explain how to determine when an almost contact structure induces a contact structure, followed by examples of a manifold with a closed G₂-structure.