Cheeger Gromoll type metrics on the tangent bundle

In this paper we study a Riemanian metric on the tangent bundle $T(M)$ of a Riemannian manifold $M$ which generalizes the Cheeger Gromoll metric and a compatible almost complex structure which together with the metric confers to $T(M)$ a structure of locally conformal almost K\"ahlerian manifold. We found conditions under which $T(M)$ is almost K\"ahlerian, locally conformal K\"ahlerian or K\"ahlerian or when $T(M)$ has constant sectional curvature or constant scalar curvature.Comment: 9 pages. to appear in Proceedings of fifth international symposium BioMathsPhys, Iasi, June 16-17, 200

On the Geometry of Constant Angle Surfaces in Sol3Sol_3

In this paper we classify all surfaces in the 3-dimensional Lie group $Sol_3$ whose normals make constant angle with a left invariant vector field.Comment: 13 pages with 4 figure

Constant angle surfaces in Minkowski space

A constant angle surface in Minkowski space is a spacelike surface whose unit normal vector field makes a constant hyperbolic angle with a fixed timelike vector. In this work we study and classify these surfaces. In particular, we show that they are flat. Next we prove that a tangent developable surface (resp. cylinder, cone) is a constant angle surface if and only if the generating curve is a helix (resp. a straight-line, a circle).Comment: 19 pages, 6 figure

Minimal translation surfaces in Sol3Sol_3

In the homogeneous space Sol$_3$, a translation surface is parameterized by $x(s,t)=\alpha(s)\ast\beta(t)$, where $\alpha$ and $\beta$ are curves contained in coordinate planes and $\ast$ denotes the group operation of Sol$_3$. In this paper we study translation surfaces in Sol$_3$ whose mean curvature vanishes.Comment: 18 page

Gray Curvature Identities for Almost Contact Metric Manifolds

The aim of this research is the study of Gray curvature identities, introduced by Alfred Gray in \cite{kn:Gra76} for the class of almost hermitian manifolds. As known till now, there is no equivalent for the class of almost contact manifolds. For this purpose we use the Boohby-Wang fibration and the warped manifolds construction in order to establish which identities could be satisfied by an almost contact manifold.Comment: 13 page

Geometry of PR-warped products in para-Kaehler manifolds

In this paper, we initiate the study of \p R-warped products in para-K\"ahler manifolds and prove some fundamental results on such submanifolds. In particular, we establish a general optimal inequality for \p R-warped products in para-K\"ahler manifolds involving only the warping function and the second fundamental form. Moreover, we completely classify \p R-warped products in the flat para-K\"ahler manifold with least codimension which satisfy the equality case of the inequality.Comment: 28 page

On the Geometry of the Second Fundamental Form of Translation Surfaces in E3

In this paper we study the second fundamental form of translation surfaces in E3. We give a non-existence result for polynomial translation surfaces in E3 with vanishing second Gaussian curvature KII. We classify those translation surfaces for which KII and H are proportional. Finally we obtain that there are no II-minimal translation surfaces in the Euclidean 3-space.Comment: 15 pages, 6 figure

Polynomial Translation Weingarten Surfaces in 3-dimensional Euclidean space

In this paper we will classify those translation surfaces in E3 involving polynomials which are Weingarten surfaces. We analyze Weingarten translation surfaces satisfying 2aH + bK = 0. We study also other types of translation surfaces, involving power functions, for which the second Gaussian curvature vanishes.Comment: 8 pages, 5 figures, presented as poster at the VIII International Colloquium on Differential Geometry, Santiago de Compostela, Spain, 7-11 July 2008; ISBN 978-981-426116

A New Approach on Constant Angle Surfaces in E^3

In this paper we study constant angle surfaces in Euclidean 3-space. Even that the result is a consequence of some classical results involving the Gauss map (of the surface), we give another approach to classify all surfaces for which the unit normal makes a constant angle with a fixed direction.Comment: 9 pages, 4 figure

Periodic magnetic curves in elliptic Sasakian space forms

It is an interesting question whether a given equation of motion has a periodic solution or not, and in the positive case to describe them. We investigate periodic magnetic curves in elliptic Sasakian space forms and we obtain a quantization principle for periodic magnetic flowlines on Berger spheres. We give a criterion for periodicity of magnetic curves on the unit sphere ${\mathbb{S}}^3$.Comment: 14 pages, 3 figure