Submanifolds of Kaehlerian manifold with a metric compound structure of rank 2

Summary The metric compound structure of rank r is an obstructed structure of an induced structure on a real submanifold in an almost Hermitian manifold. In this paper we deal with a submanifold with metric compound structure of rank 2 in a Kaehlerian manifold and we classify it under some suitable conditions. Namely it is a standard sphere or neither Einstein nor conformally flat.     

A classification of almost contact metric manifolds

Summary It is obtained a complete classification for almost contact metric manifolds through the study of the covariant derivative of the fundamental 2- form on those manifolds.This work was supported by the « Consejería de Educación del Gobierno de Canarias ».     

Harmonicity on some almost contact metric manifolds

In this paper we shall study some classes of harmonic maps on Trans-Sasakian manifolds.     

Riemannian submersions from almost contact metric manifolds

In this paper we obtain the structure equation of a contact-complex Riemannian submersion and give some applications of this equation in the study of almost cosymplectic manifolds with Kähler fibres.     

On the classification of almost contact metric manifolds

On connected manifolds of dimension higher than three, the non-existence of 132 Chinea and González-Dávila types of almost contact metric structures is proved. This is a consequence of some interrelations among components of the intrinsic torsion of an almost contact metric structure. Such interrelations allow to describe the exterior derivatives of some relevant forms in the context of almost contact metric geometry.     

Geometric properties of almost contact metric 3-submersions

Summary In this paper, we discuss some geometric properties of three types of Riemannian submersions whose total space is an almost contact metric manifold with 3-structure. The study is focused on the transference of structures.     

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.     

Some classes of almost contact metric manifolds and contact Riemannian submersions

Locally conformal almost quasi-Sasakian manifolds are related to the Chinea--Gonzales classification of almost contact metric manifolds. It follows that these manifolds set up a wide class of almost contact metric manifolds containing several interesting subclasses. Contact Riemannian submersions whose total space belongs to each of the considered classes are then investigated. The explicit expression of the integrability tensor and of the mean curvature vector field of each fibre are given. This allows us to state the integrability of the horizontal distribution and/or the minimality of the fibres in particular cases. The classes of the base space and of the fibres are also determined, so extending several well-known results.     

Harmonicity on maps between almost contact metric manifolds

We study (φ,φ′)-holomorphic maps between almost contact metric manifolds, in particular horizontally conformal (φ,φ′)-holomorphic submersions, and obtain some criteria for the harmonicity of such maps.     

On almost contact metric hypersurface of a Kahler manifold

We have studied the normality of an almost contact metric hypersurface of a Kahler manifold. Quasi-umbilical and umbilical properties have also been studied.     

Invariants of conformal transformations of almost contact metric structures

The so-called structure tensors of almost contact metric structures, which play a key role in the geometry of almost contact metric structures, are explicitly calculated. The transformations of these tensors under conformal transformations of almost contact metric structures are described. The results obtained are used to study the behavior of the most interesting classes of almost contact structures under conformal transformations.     

Nilpotent groups admitting an almost regular automorphism of order four

We consider locally nilpotent periodic groups admitting an almost regular automorphism of order 4. The following are results are proved: (1) If a locally nilpotent periodic group G admits an automorphism ϕ of order 4 having exactly m<∞ fixed points, then (a) the subgroup {ie176-1} contains a subgroup of m-bounded index in {ie176-2} which is nilpotent of m-bounded class, and (b) the group G contains a subgroup V of m-bounded index such that the subgroup {ie176-3} is nilpotent of m-bounded class (Theorem 1); (2) If a locally nilpotent periodic group G admits an automorphism ϕ of order 4 having exactly m<∞ fixed points, then it contains a subgroup V of m-bounded index such that, for some m-bounded number f(m), the subgroup {ie176-4}, generated by all f(m) th powers of elements in {ie176-5} is nilpotent of class ≤3 (Theorem 2). Supported by RFFR grant No. 94-01-00048 and by ISF grant NQ7000. Translated fromAlgebra i Logika, Vol. 35, No. 3, pp. 314–333, May–June, 1996.     

Polycyclic group admitting an almost regular automorphism of prime order

A well-known result due to Thompson states that if a finite group G has a fixed-point-free automorphism of prime order, then G is nilpotent. In this note, giving a counterpart of Thompson's result in the context of polycyclic groups, we prove: if a polycyclic group G has an automorphism of prime order with finitely many fixed points, then G is nilpotent-by-finite.