A Class of 3-dimensional Contact Metric Manifolds

We classify the contact metric 3-manifolds such that ${||{\rm grad}{\lambda}|| = 1 \, {\rm and} \, \nabla{\xi}{\tau} = 2a{\tau}{\phi}}$ .     

Vranceanu surface in $$ \mathbb{E}^4 $$ with pointwise 1- type Gauss map

In this article we investigate Vranceanu rotation surfaces with pointwise 1- type Gauss map in Euclidean 4-space $ \mathbb{E}^4 $ \mathbb{E}^4 . We show that a Vranceanu rotation surface M has harmonic Gauss map if and only if M is a part of a plane. Further, we give necessary and sufficent conditions for Vranceanu rotation surface to have pointwise 1-type Gauss map.     

Multiwalled boron nitride microtubes (BNMTs) shielding in thermal neutron absorbing

In this study, multiwalled boron nitride microtubes (BNMTs) were synthesised from amorphous boron powder in pure nitrogen atmosphere controlled graphite furnace at 1300°C for 6?h with amorphous boron/manganese (IV) oxide (MnO₂) catalyst mass ratio of 1/1. It was found that the synthesised BNMTs outer diameters and the lengths vary between 0.68 and 1.57?µm and between 6.79 and 31.23?µm, respectively, by the scanning electron microscope analysis. The surface layer of AISI 1040 steel material was coated with multiwalled BNMTs at 950°C for 4?h in a foundry furnace. Transport phenomena of BNMT molecules on surfaces of the steel were considered by diffusion. Neutrons from obtained ²⁴¹Am-Be source were irradiated on the ⁵⁸Fe nuclei. The irradiation properties of the without and with BNMT coated steel materials were studied in the field of gamma emitted by ⁶⁰Co. The radiation exposure rate of gamma radiation sources used at 1099 and 1291?keV, respectively. The higher peak area was obtained in steel coated with BNMT according to non-coated steel from irradiation results of samples. These results show that BNMT coated steel was more capable for radiation shielding.     

On generalized recurrent Riemannian manifolds

The object of the present paper is to study a type of Riemannian manifolds called generalized recurrent manifolds. We have constructed two concrete examples of such a manifold whose scalar curvature is non-zero non-constant. Some other properties have been considered. Among others it is shown that on a generalized recurrent manifold with constant scalar curvature, Weyl-semisymmetry and semisymmetry are equivalent. Sufficient condition for a generalized recurrent manifold to be a special quasi Einstein manifold is obtained.     

ON PSEUDOSYMMETRY TYPE HYPERSURFACES OF SEMI-EUCLIDEAN SPACES Ⅰ

In this paper the authors investigate hypersurfaces M of a semi-Euclidean space Esn+1, n ≥ 4, satisfying (aC +βR). H ＝ LkQ(g, Hk), k ＝ 1,2,3. Using obtained results they show additional curvature properties of investigated hypersurfaces.     

Almost f-Cosymplectic Manifolds

The purpose of this paper is to study a new class of contact manifolds. Such manifolds are called almost f-cosymplectic manifolds. Several tensor conditions are studied for such type of manifolds. We conclude our results with two examples of almost f-cosymplectic manifolds.     

On the Existence of Proper Nearly Kenmotsu Manifolds

We prove that a nearly Kenmotsu manifold is locally isometric to the warped product of a real line and a nearly Kähler manifold. As consequence, a normal nearly Kenmotsu manifold is Kenmotsu. Furthermore, we show that there do not exist nearly Kenmotsu hypersurfaces of nearly Kähler manifolds.

     

C-Totally real pseudo-parallel submanifolds of Sasakian space forms

Let be (2n + 1)-dimensional Sasakian space form of constant ϕ-sectional curvature (c) and M ⁿ be an ⁿ -dimensional C-totally real, minimal submanifold of . We prove that if M ⁿ is pseudo-parallel and , then M ⁿ is totally geodesic.