En este trabajo, damos el cálculo de longitudes de curvas y n-medidas de n-superficies contenidas en un grupo de LIE, por un procedimiento original. Por construcción estas medidas son invariantes a izquierda por elementos de G (Grupo de LIE ambiente). A continua ... En el cálculo de estas medidas, hemos partido de las definiciones de vector...
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November 27, 2014 (v1)PublicationUploaded on: December 4, 2022
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October 31, 2018 (v1)Publication
In this paper, the geometry of certain anti-invariant submanifolds of an S-manifold, namely those which are normal to the structure vector fields, is studied.
Uploaded on: March 27, 2023 -
May 27, 2016 (v1)Publication
We obtain a variable reduction principle for the Willmore variational problem in an ample class of conformal structures on S2n+1. This variational problem is transformed into another one, associated with an elastic-energy functional with potential, on spaces of curves in CP n. Then, we give a simple method to construct Willmore tori in certain...
Uploaded on: March 27, 2023 -
May 27, 2016 (v1)Publication
In this note a classification theorem for totally f-umbilical submanifolds of an S-space form is obtained.
Uploaded on: March 27, 2023 -
December 12, 2016 (v1)Publication
In this paper, some properties of the geometry of pseudo-Einstein hypersurfaces of the S-manifold ℋ 2n+s are studied and a theorem concerning their principal curvatures is obtained.
Uploaded on: December 4, 2022 -
October 7, 2016 (v1)Publication
The model of a massless relativistic particle with curvature-dependent Lagrangian is well known in (d+1)-dimensional Minkowski space. For other gravitational fields less rigid than those with constant (zero) curvature only a few results are known. In this paper, we give a geometric approach in order to solve the field equations associated with...
Uploaded on: December 4, 2022 -
December 16, 2016 (v1)Publication
In this paper, the notion of ξ-conformally flat on a contact metric structure is introduced and it is proved that any K-contact metric manifold is ξ-conformally flat if and only if it is an η-Einstein Sasakian manifold. Finally, some applications are given.
Uploaded on: December 5, 2022 -
October 4, 2016 (v1)Publication
In this note we shall study the notions of isotropic and marginally trapped surface in a spacetime by using a differential geometric approach. We first consider spacelike isotropic surfaces in a Lorentzian manifold and, in particular, in a four-dimensional spacetime, where the isotropy function appears to be determined by the mean curvature...
Uploaded on: March 27, 2023 -
October 19, 2016 (v1)Publication
Several notions of isotropy of a (pseudo)Riemannian manifold have been introduced in the literature, in particular, the concept of pseudo-isotropic immersion. The aim of this paper is to look more closely at this notion of pseudoisotropy and then to study the rigidity of this class of immersion into the pseudo-Euclidean space. It is worth...
Uploaded on: December 4, 2022 -
October 7, 2016 (v1)Publication
In this paper we define the contact number of a pseudo-Riemannian submanifold into the pseudo-Euclidean space, and prove that this contact number is closely related to the notion of pseudo-isotropic submanifold. We give a classification of hypersurfaces into the pseudo-Euclidean space with contact number at least 3. A classification of the...
Uploaded on: March 27, 2023 -
October 19, 2016 (v1)Publication
The family of all the submanifolds of a given Riemannian or pseudo-Riemannian manifold is large enough to classify them into some interesting subfamilies such as minimal (maximal), totally geodesic, Einstein, etc. Most of these have been extensively studied by many authors, but as far as we know, no paper has hitherto been published on the...
Uploaded on: December 4, 2022 -
October 19, 2016 (v1)Publication
We first present a geometrical approach to magnetic fields in three-dimensional Riemannian manifolds, because this particular dimension allows one to easily tie vector fields and 2-forms. When the vector field is divergence free, it defines a magnetic field on the manifold whose Lorentz force equation presents a simple and useful form. In...
Uploaded on: March 27, 2023 -
October 19, 2016 (v1)Publication
In this short note we give a simple proof of the existence of an almost contact metric structure on any orientable 3-dimensional Riemannian manifold (M3, g) with the prescribed metric g as the adapted metric of the almost contact metric structure. By using the key formula for the structure tensor obtained in the proof of this theorem, we give...
Uploaded on: March 27, 2023 -
November 21, 2016 (v1)Publication
In this paper, we present the existence and uniqueness theorems for slant immersions into Sasakian-space-forms. By applying the first result, we prove several existence theorems for slant submanifolds. In particular, we prove the existence theorems for three-dimensional slant submanifolds with prescribed mean curvature or with prescribed scalar...
Uploaded on: December 4, 2022 -
December 16, 2016 (v1)Publication
In this paper, we study the possibility of obtaining an induced contact metric structure on a slant submanifold of a contact metric manifold. We also give a characterization theorem for three-dimensional slant submanifolds.
Uploaded on: December 4, 2022 -
October 19, 2016 (v1)Publication
We define and study both bi-slant and semi-slant submanifolds of an almost contact metric manifold and, in particular, of a Sasakian manifold. We prove a characterization theorem for semi-slant submanifolds and we obtain integrability conditions for the distributions which are involved in the definition of such submanifolds. We also study an...
Uploaded on: December 4, 2022 -
November 21, 2016 (v1)Publication
We study the relationship between slant submanifolds in both Complex and Contact Geometry through Riemannian submersions. We present some construction procedures to obtain slant submanifolds in the unit sphere and in a Stiefel manifold. We also generalize them by means of the Boothby-Wang fibration. Finally, we show some characterization...
Uploaded on: March 27, 2023 -
July 21, 2016 (v1)Publication
We introduce the notion of Gauss-Landau-Hall magnetic field on a Riemannian surface. The corresponding Landau-Hall problem is shown to be equivalent to the dynamics of a massive boson. This allows one to view that problem as a globally stated, variational one. In this framework, flowlines appear as critical points of an action with density...
Uploaded on: March 27, 2023 -
October 7, 2016 (v1)Publication
We exhibit a variational approach to study the magnetic flow associated with a Killing magnetic field in dimension 3. In this context, the solutions of the Lorentz force equation are viewed as Kirchhoff elastic rods and conversely. This provides an amazing connection between two apparently unrelated physical models and, in particular, it ties...
Uploaded on: December 4, 2022