On Kodaira dimension of almost complex 4-dimensional solvmanifolds without complex structures

The aim of this paper is to continue the study of Kodaira dimension for almost complex manifolds, focusing on the case of compact [Formula: see text]-dimensional solvmanifolds without any integrable almost complex structure. According to the classification theory we consider: [Formula: see text], [Formula: see text] and [Formula: see text] with [Formula: see text]. For the first solvmanifold we introduce special families of almost complex structures, compute the corresponding Kodaira dimension and show that it is no longer a deformation invariant. Moreover, we prove Ricci flatness of the canonical connection for the almost Kähler structure. Regarding the other two manifolds we compute the Kodaira dimension for certain almost complex structures. Finally, we construct a natural hypercomplex structure providing a twistorial description.

S.-S. Chern’s study of almost-complex structures on the six-sphere

In April 2003, Chern began a study of almost-complex structures on the six-sphere, with the idea of exploiting the special properties of its well-known almost-complex structure invariant under the exceptional group [Formula: see text]. While he did not solve the (currently still open) problem of determining whether there exists an integrable almost-complex structure on [Formula: see text], he did prove a significant identity that resolves the question for an interesting class of almost-complex structures on [Formula: see text].

Kahlerian manifolds related in H-projective recurrent curvature killing vector fields with vectorial fields

Izumi and Kazanari [2], has calculated and defined on infinitesimal holomorphically projective transformations in compact Kaehlerian manifolds. Also, Malave Guzman [3], has been studied transformations holomorphic ammeters projective equivalentes. After that, Negi [5], have studied and considered some problems concerning Pseudo-analytic vectors on Pseudo-Kaehlerian Manifolds. Again, Negi, et. al. [6],has defined and obtained an analytic HP-transformation in almost Kaehlerian spaces. In this paper we have measured and calculated a Kahlerian manifolds related in H-projective recurrent curvature killing vector fields with vectorial fields and their holomorphic propertiesEinsteinian and the constant curvature manifoldsare established.Kaehlerian holomorphically projective recurrent curvature manifolds with almost complex structures by using the geometrical properties of the harmonic and scalar curvatures calculated overkilling vectorial fieldsare obtained

Some Properties on Divine Kaehlerian Manifold

Fibonacci sequence and the divine ratio are intimately inter-connected. In the Fibonacci sequence each number is the sum of previous two consecutive numbers and the ratio of any two consecutive numbers reflects the approximate value of divine ratio. The relationship between divine ratio and Fibonacci series is well express in divergent faunal anatomy and floral as well as their morphology. The present article is intended to study the properties of divine Kaehlerian manifold in terms of Fibonacci sequence, trace & eigen values of divine structure including its almost complex structures. Some properties of induced structures, theorems and propositions related to it have also been studied.