scholarly journals New Cartan’s tensors and pseudotensors in a generalized Finsler space

Filomat ◽  
2014 ◽  
Vol 28 (1) ◽  
pp. 107-117
Author(s):  
Milica Cvetkovic ◽  
Milan Zlatanovic
Keyword(s):  
Covariant Derivative ◽  
Finsler Space ◽  
Differentiable Manifold ◽  
Curvature Tensors

In this work we defined a generalized Finsler space (GFN) as 2N-dimensional differentiable manifold with a non-symmetric basic tensor gij(x,x?), which applies that gij_?|m(x,x?)=0; ?=1,2. Based on non-symmetry of basic tensor, we obtained ten Ricci type identities, comparing to two kinds of covariant derivative of a tensor in Rund?s sense. There appear two new curvature tensors and fifteen magnitudes, we called ?curvature pseudotensors?.

scholarly journals Identities for curvature tensors in generalized Finsler space

Filomat ◽  
2009 ◽  
Vol 23 (2) ◽  
pp. 34-42 ◽  
Author(s):  
Milan Zlatanovic ◽  
Svetislav Mincic
Keyword(s):  
Finsler Space ◽  
Cyclic Symmetry ◽  
Symmetric Connection ◽  
Two Indices ◽  
Curvature Tensors

In the some previous works we have obtained several curvature tensors in the generalized Finsler space GFN (the space with non-symmetric basic tensor and non-symmetric connection in Rund's sence). In this work we study identities for the mentioned tensors (the antisymmetriy with respect of two indices, the cyclic symmetry, the symmetry with respect of pairs of indices).

scholarly journals THE STRUCTURE OF ALGEBRAIC COVARIANT DERIVATIVE CURVATURE TENSORS

2004 ◽  
Vol 01 (06) ◽  
pp. 711-720 ◽  
Author(s):  
J. DÍAZ-RAMOS ◽  
B. FIEDLER ◽  
E. GARCÍA-RÍO ◽  
P. GILKEY
Keyword(s):  
Covariant Derivative ◽  
Embedding Theorem ◽  
Curvature Tensors ◽  
Nash Embedding Theorem

We use the Nash embedding theorem to construct generators for the space of algebraic covariant derivative curvature tensors.

scholarly journals Hypersurfaces Of a Finsler Space

1956 ◽  
Vol 8 ◽  
pp. 487-503 ◽  
Author(s):  
Hanno Rund
Keyword(s):  
Classical Theory ◽  
Covariant Derivative ◽  
Present Author ◽  
Finsler Space ◽  
Metric Tensor

Introduction. Certain aspects of the theory of subspaces of a Finsler space had been treated by the present author in earlier papers (7). These developments were based on an approach essentially different from the classical theory of Cartan (2) and subsequent writers, whose use of the element of support enables one to introduce the so-called “euclidean connection,” which effects the vanishing of the covariant derivative of the metric tensor.

scholarly journals On Generalized h-Recurrent Finsler Connection

2021 ◽  
Vol 2 (1) ◽  
pp. 35-42
Author(s):  
Khageshwar Mandal
Keyword(s):  
Covariant Derivative ◽  
Curvature Tensors

The purpose of the present paper is to generalize the concept of recurrent Finsler connection by taking h-connection by applying h-covariant derivative of Φ (p)ij as recurrent. Such a connection will be called a generalized h-recurrent Finsler connection. The relation between curvature tensors of Cartan's connection Cτ and generalized h-recurrent Finsler connection has been established.

Subspaces of a Generalized Metric Space

1959 ◽  
Vol 11 ◽  
pp. 235-255 ◽  
Author(s):  
H. A. Eliopoulos
Keyword(s):  
Differential Geometry ◽  
Metric Space ◽  
Finsler Space ◽  
Tangent Vector ◽  
Differentiable Manifold ◽  
Finsler Metric ◽  
Generalized Metric Space ◽  
System Of Equations ◽  
Generalized Metric

In a paper published in 1956, Rund (4) developed the differential geometry of a hypersurface of n— 1 dimensions imbedded in a Finsler space of n dimensions, considered as locally Minkowskian.The purpose of the present paper is to provide an extension of the results of (4) and thus develop a theory for the case of m-dimensional subspaces imbedded in a generalized (Finsler) metric space.We consider an n-dimensional differentiable manifold Xn and we restrict our attention to a suitably chosen co-ordinate neighbourhood of Xn in which a co-ordinate system xi (i= 1, 2, … , n), is defined. A system of equations of the type xi = xi(t) defines a curve C of Xn the tangent vector dxi/dt of which is denoted by xi.

scholarly journals Recurrence Decompositions in Finsler Space

2020 ◽  
Vol 1 (1) ◽  
pp. 77-86
Author(s):  
Adel M. A. Al-Qashbari
Keyword(s):  
Differential Geometry ◽  
Covariant Derivative ◽  
Finsler Space ◽  
Applied Mathematics ◽  
Torsion Tensor ◽  
Finsler Geometry ◽  
Second Order ◽  
Connected Space ◽  
Projective Curvature Tensor ◽  
Affinely Connected Space

Finsler geometry is a kind of differential geometry originated by P. Finsler. Indeed, Finsler geometry has several uses in a wide variety and it is playing an important role in differential geometry and applied mathematics of problems in physics relative, manual footprint. It is usually considered as a generalization of Riemannian geometry. In the present paper, we introduced some types of generalized $W^{h}$ -birecurrent Finsler space, generalized $W^{h}$ -birecurrent affinely connected space and we defined a Finsler space $F_{n}$ for Weyl's projective curvature tensor $W_{jkh}^{i}$ satisfies the generalized-birecurrence condition with respect to Cartan's connection parameters $\Gamma ^{\ast i}_{kh}$, such that given by the condition (\ref{2.1}), where $\left\vert m\right. \left\vert n\right. $ is\ h-covariant derivative of second order (Cartan's second kind covariant differential operator) with respect to $x^{m}$ \ and $x^{n}$ ,\ successively, $\lambda _{mn}$ and $\mu _{mn~}$ are\ non-null covariant vectors field and such space is called as a generalized $W^{h}$ -birecurrent\ space and denoted briefly by $GW^{h}$ - $BRF_{n}$ . We have obtained some theorems of generalized $W^{h}$ -birecurrent affinely connected space for the h-covariant derivative of the second order for Wely's projective torsion tensor $~W_{kh}^{i}$ , Wely's projective deviation tensor $~W_{h}^{i}$ in our space. We have obtained the necessary and sufficient condition forsome tensors in our space.

scholarly journals Some relations in the generalized Kählerian spaces of the second kind

Filomat ◽  
2009 ◽  
Vol 23 (2) ◽  
pp. 82-89 ◽  
Author(s):  
Mica Stankovic ◽  
Ljubica Velimirovic ◽  
Milan Zlatanovic
Keyword(s):  
Covariant Derivative ◽  
Riemannian Space ◽  
Complex Structure ◽  
Almost Complex Structure ◽  
Generalized Riemannian Space ◽  
Almost Complex ◽  
Definition Of ◽  
Curvature Tensors

Starting from the definition of generalized Riemannian space (GRN) [1], in which a non-symmetric basic tensor Gij is introduced, in the present paper a generalized K?hlerian space GK2 N of the second kind is defined, as a GRN with almost complex structure Fhi, that is covariantly constant with respect to the second kind of covariant derivative (equation (2.3)). Several theorems are proved. These theorems are generalizations of the corresponding theorems relating to KN. The relations between Fhi and four curvature tensors from GRN are obtained.

scholarly journals On some properties of non-symmetric connections

Filomat ◽  
2015 ◽  
Vol 29 (3) ◽  
pp. 585-591
Author(s):  
Svetislav Mincic
Keyword(s):  
Covariant Derivative ◽  
Dimensional Manifold ◽  
Symmetric Connection ◽  
Curvature Tensors

On an N-dimensional manifold with non-symmetric connection Lijk four kinds of covariant derivative (1.1) are defined, and four curvature tensors are obtained. In the present paper specially the 3rd and the 4th kind of covariant derivative are studied, particularly their application on ?-symbols.

DE RHAM WAVE EQUATION FOR TENSOR VALUED p-FORMS

2003 ◽  
Vol 12 (08) ◽  
pp. 1363-1384 ◽  
Author(s):  
DONATO BINI ◽  
CHRISTIAN CHERUBINI ◽  
ROBERT T. JANTZEN ◽  
REMO RUFFINI
Keyword(s):  
General Relativity ◽  
Black Hole ◽  
Wave Equation ◽  
Covariant Derivative ◽  
Differential Forms ◽  
Black Hole Spacetimes ◽  
Metric Connection ◽  
De Rham ◽  
Integral Spin ◽  
Curvature Tensors

The de Rham Laplacian Δ (dR) for differential forms is a geometric generalization of the usual covariant Laplacian Δ, and it may be extended naturally to tensor-valued p-forms using the exterior covariant derivative associated with a metric connection. Using it the wave equation satisfied by the curvature tensors in general relativity takes its most compact form. This wave equation leads to the Teukolsky equations describing integral spin perturbations of black hole spacetimes.

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