Some remarks on R-contact flows

2015

In this paper, we prove that evry 3-dimensional manifold M is a ∅-recurrent N(k)-contact metric manifold if and only if it is flat. Then we classify the ∅-recurrent contact metric manifolds of constant curvature. This implies that there exists no ∅-recurrent N(k)-contact metric manifold, which is neither symmetric nor locally ∅-symmetric

Thai Journal of Mathematics, 2012

The tensor h = 1 2 L ξ φ, L denotes the Lie derivative, plays a crucial role to determine the nature of a (k, µ)-contact metric manifold. The object of the present paper is to study (k, µ)-contact metric manifolds for which the tensor h is parallel, recurrent and cyclically parallel. Three-dimensional (k, µ)-contact metric manifolds with η-recurrent Ricci tensor have been studied. Illustrative examples, related to the results obtained in each section, are also given.

The object of the present paper is to study torseforming vector field in a 3-dimensional contact metric manifold with Qϕ = ϕQ. Here we prove that the torseforming vector field in a 3-dimensional contact metric manifold with Qϕ = ϕQ is a concircular vector field.

Hacettepe Journal of Mathematics and Statistics, 2012

In this paper we generalize the results of Tanno and Zhen. Then we study the cyclic parallel Ricci tensor on a K-contact manifold.

Kodai Mathematical Journal, 1991

in a paper of 1985 [5] studied a kind of Dirichlet energy in terms of the torsion τ(τ=Xξg) of a 3-dimensional compact contact manifold and a problem analogous to the Yamabe problem. They raised the question of determining all 3-dimensional contact manifolds with τ-Q (i.e. K-contact). In a long paper of 1989 [8] S. Tanno studied the Dirichlet energy and gauge transformations of contact manifolds. D. E. Blair [2] obtained the critical point condition of I(g)=\ Ric(ξ)dV g over JM(η) (the space of all the as-J M

2004

We consider a skew symetric conformal vector fleld on a closed concircu- lar almost contact manifold M and flnd its properties. Also, for a CR-product submanifold M0 of M, the mean curvature vector fleld of the invariant subman- ifold and the ∞atness of the antiinvariant submanifold are studied, under the assumption that M0 admits a skew symmetric Killing vector fleld tangent to the invariant submanifold, such that its generative is tangent to the antiinvariant submanifold.

International Journal of Mathematics and Mathematical Sciences, 1990

A new class of contact manifolds (carrlng a global non-vanlshlng tlmellke vector field) is introduced to establish a relation between spacetlme manifolds and contact structures.

SUT Journal of Mathematics

The object of this paper is to study K-contact manifolds with quasiconformal curvature tensor. We characterised K-contact manifolds satisfying certain curvature conditions on the quasi-conformal curvature tensor.

Mediterranean Journal of Mathematics, 2013

We consider manifolds endowed with metric contact pairs for which the two characteristic foliations are orthogonal. We give some properties of the curvature tensor and in particular a formula for the Ricci curvature in the direction of the sum of the two Reeb vector fields. This shows that metrics associated to normal contact pairs cannot be flat. Therefore flat non-Kähler Vaisman manifolds do not exist. Furthermore we give a local classification of metric contact pair manifolds whose curvature vanishes on the vertical subbundle. As a corollary we have that flat associated metrics can only exist if the leaves of the characteristic foliations are at most three-dimensional.

Mathematical journal of Okayama University, 2015

In this paper, we prove that evry 3-dimensional manifold M is a φ-recurrent N (k)-contact metric manifold if and only if it is flat. Then we classify the φ-recurrent contact metric manifolds of constant curvature. This implies that there exists no φ-recurrent N (k)-contact metric manifold, which is neither symmetric nor locally φ-symmetric.