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.     

The Albanese mapping for compact almost complex manifolds

Partially supported by the Forschungsinstitut für Mathematik at the ETH Zuerich     

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)].     

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.     

On the geometry of model almost complex manifolds with boundary

We study some special almost complex structures on strictly pseudoconvex domains in ℝ^{2 n} . They appear naturally as limits under a nonisotropic scaling procedure and play a role of model objects in the geometry of almost complex manifolds with boundary. We determine explicitely some geometric invariants of these model structures and derive necessary and sufficient conditions for their integrability. As applications we prove a boundary extension and a compactness principle for some elliptic diffeomorphisms between relatively compact domains.     

Some lightlike submanifolds of almost complex manifolds with Norden metric

In this paper we study submanifolds of an almost complex manifold with Norden metric which are non-degenerate with respect to the one Norden metric and lightlike with respect to the other Norden metric on the manifold. Relations between the induced geometric objects of some of these submanifolds are given. Examples of the considered submanifolds are constructed.