Different structures on subspaces of OsckM

Irena Comic; Radu Miron

doi:10.2298/tam1301027c

Different structures on subspaces of OsckM

Theoretical and Applied Mechanics ◽

10.2298/tam1301027c ◽

2013 ◽

Vol 40 (1) ◽

pp. 27-48

Author(s):

Irena Comic ◽

Radu Miron

Keyword(s):

Vector Fields ◽

Ambient Space

The geometry of OsckM spaces was introduced by R. Miron and Gh. Atanasiu in [6] and [7]. The theory of these spaces was developed by R. Miron and his cooperators from Romania, Japan and other countries in several books and many papers. Only some of them are mentioned in references. Here we recall the construction of adapted bases in T(OsckM) and T*(OsckM), which are comprehensive with the J structure. The theory of two complementary family of subspaces is presented as it was done in [2] and [4]. The operators J,?J, ?,??, p, p* are introduced in the ambient space and subspaces. Some new relations between them are established. The action of these operators on Liouville vector fields are examined.

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A link between harmonicity of 2-distance functions and incompressibility of canonical vector fields

Tamkang Journal of Mathematics ◽

10.5556/j.tkjm.49.2018.2804 ◽

2018 ◽

Vol 49 (4) ◽

pp. 339-347

Author(s):

Bang-Yen Chen

Keyword(s):

Riemannian Manifold ◽

Vector Field ◽

Distance Function ◽

Vector Fields ◽

Sufficient Conditions ◽

Tangential Component ◽

Ambient Space ◽

Distance Functions ◽

Necessary And Sufficient ◽

Canonical Vector

Let $M$ be a Riemannian submanifold of a Riemannian manifold $\tilde M$ equipped with a concurrent vector field $\tilde Z$. Let $Z$ denote the restriction of $\tilde Z$ along $M$ and let $Z^T$ be the tangential component of $Z$ on $M$, called the canonical vector field of $M$. The 2-distance function $\delta^2_Z$ of $M$ (associated with $Z$) is defined by $\delta^2_Z=\$. In this article, we initiate the study of submanifolds $M$ of $\tilde M$ with incompressible canonical vector field $Z^T$ arisen from a concurrent vector field $\tilde Z$ on the ambient space $\tilde M$. First, we derive some necessary and sufficient conditions for such canonical vector fields to be incompressible. In particular, we prove that the 2-distance function $\delta^2_Z$ is harmonic if and only if the canonical vector field $Z^T$ on $M$ is an incompressible vector field. Then we provide some applications of our main results.

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Scalar–spinor fields interaction in de Sitter ambient space formalism

Modern Physics Letters A ◽

10.1142/s0217732319502055 ◽

2019 ◽

Vol 34 (25) ◽

pp. 1950205 ◽

Cited By ~ 1

Author(s):

Y. Ahmadi ◽

F. Jalilifard ◽

M. V. Takook

Keyword(s):

Scalar Field ◽

Vector Fields ◽

Ambient Space ◽

Tree Level ◽

Matrix Elements ◽

De Sitter ◽

Field Interaction ◽

Spinor Fields ◽

Space Formalism ◽

Vector Formula

In de Sitter ambient space formalism, the massless minimally coupled scalar field can be constructed from a massless conformally coupled scalar field and a constant five-vector [Formula: see text]. Also, a constant five-vector [Formula: see text] appears in the interaction Lagrangian of massless minimally coupled scalar and spinor fields in this formalism. These constant five-vector fields can be fixed in the interaction case in the null curvature limit. Here, we will calculate the [Formula: see text] matrix elements of scalar–spinor field interaction in the tree level approximation. Then the constant five-vectors [Formula: see text] and [Formula: see text], will be fixed by comparing the [Formula: see text] matrix elements in the null curvature limits with the Minkowskian counterparts.

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Topological equivalence for multiple saddle connections

Anais da Academia Brasileira de Ciências ◽

10.1590/s0001-37652002000400002 ◽

2002 ◽

Vol 74 (4) ◽

pp. 577-584 ◽

Cited By ~ 1

Author(s):

CLEMENTA ALONSO ◽

MARIA IZABEL CAMACHO ◽

FELIPE CANO

Keyword(s):

Vector Fields ◽

Ambient Space ◽

Topological Equivalence ◽

Degeneracy Condition

We study the topological equivalence between two vector fields defined in the neighborhood of the skeleton of a normal crossings divisor in an ambient space of dimension three. We deal with singularities obtained from local ones by ambient blowing-ups: we impose thus the non-degeneracy condition that they are all hyperbolic without certain algebraic resonances in the set of eigenvalues. Once we cut-out the attractors, we get the result if the corresponding graph has no cycles. The case of cycles is of another nature, as the Dulac Problem in dimension three.

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