scholarly journals Generalized Riemannian spaces with respect to 4-velocity vectors and functions of state parameters

Filomat ◽  
2021 ◽  
Vol 35 (5) ◽  
pp. 1519-1541
Author(s):  
Nenad Vesic ◽  
Dragoljub Dimitrijevic ◽  
Dusan Simjanovic
Keyword(s):  
Metric Tensor ◽  
Cosmological Context ◽  
Metric Tensors ◽  
Riemannian Spaces

We pointed to 4-dimensional generalized Riemannian spaces important for applications in some parts of physics here. Complete metric tensors and its possibilities to be applied in cosmology are analyzed in this paper. We used the results of N. O. Vesic, presented in [14]. At the end of the paper, we studied the diagonal symmetric metric tensor in the cosmological context.

ON THE RECOVERY OF A MANIFOLD WITH PRESCRIBED METRIC TENSOR

2003 ◽  
Vol 01 (04) ◽  
pp. 433-453 ◽  
Author(s):  
CRISTINEL MARDARE
Keyword(s):  
Differential Geometry ◽  
Classical Theorem ◽  
Compatibility Conditions ◽  
Metric Tensor ◽  
Distributional Sense ◽  
Metric Tensors

A classical theorem in differential geometry asserts that if a C2-metric tensor satisfies the Riemann compatibility conditions, then it is induced by an immersion. We prove that this theorem still holds true for C1-metric tensors satisfying the Riemann compatibility conditions in a distributional sense.

scholarly journals On projective-symmetric spaces

1964 ◽  
Vol 4 (1) ◽  
pp. 113-121 ◽  
Author(s):  
Bandana Gupta
Keyword(s):  
Symmetric Space ◽  
Curvature Tensor ◽  
Symmetric Spaces ◽  
Covariant Differentiation ◽  
Metric Tensor ◽  
Projective Curvature ◽  
Projective Curvature Tensor ◽  
Image Position ◽  
Riemannian Spaces

This paper deals with a type of Remannian space Vn (n ≧ 2) for which the first covariant dervative of Weyl's projective curvature tensor is everywhere zero, that is where comma denotes covariant differentiation with respect to the metric tensor gij of Vn. Such a space has been called a projective-symmetric space by Gy. Soós [1]. We shall denote such an n-space by ψn. It will be proved in this paper that decomposable Projective-Symmetric spaces are symmetric in the sense of Cartan. In sections 3, 4 and 5 non-decomposable spaces of this kind will be considered in relation to other well-known classes of Riemannian spaces defined by curvature restrictions. In the last section the question of the existence of fields of concurrent directions in a ψ will be discussed.

scholarly journals Einstein’s Equation of motion for exterior test particles with spherical mass distribution having varied field, time and radial distance; Golden metric tensors approach.

2021 ◽  
Keyword(s):  
Gravitational Field ◽  
Polar Motion ◽  
Equations Of Motion ◽  
Radial Distance ◽  
Equation Of Motion ◽  
Metric Tensor ◽  
Test Particles ◽  
Einstein's Equation ◽  
Spherical Mass ◽  
Metric Tensors

Golden metric tensors exterior to hypothetical distribution of mass whose field varies with time and radial distance have been used to construct the coefficient of affine connections that invariably was used to obtained the Einstein’s equations of motion for test particles of non-zero rest masses. The expression for the variation of time on a clock moving in this gravitational field was derived using the time equation of motion. The test particles in this field under the condition of pure polar motion have an inverse square dependence velocity which depends on radial distance. Our result indicates that despite using the golden metric tensor, the inverse square dependence of the velocity on radial distance has not been changed.

scholarly journals On conformally recurrent spaces of second order

1969 ◽  
Vol 10 (1-2) ◽  
pp. 155-161 ◽  
Author(s):  
M. C. Chaki ◽  
A. N. Roy Chowdhury
Keyword(s):  
Curvature Tensor ◽  
Second Order ◽  
Covariant Differentiation ◽  
Metric Tensor ◽  
Conformal Curvature ◽  
Conformal Curvature Tensor ◽  
Image Position ◽  
Conformally Recurrent ◽  
Zero Vector ◽  
Riemannian Spaces

In a recent paper [1] Adati and Miyazawa studied conformally recurrent spaces, that is, Riemannian spaces defined by where is the conformal curvature tensor: λi is a non-zero vector and comma denotes covariant differentiation with respect to the metric tensor gij.

scholarly journals On equitorsion concircular tensors of generalized Riemannian spaces

Filomat ◽  
2014 ◽  
Vol 28 (3) ◽  
pp. 463-471 ◽  
Author(s):  
Milan Zlatanovic ◽  
Irena Hinterleitner ◽  
Marija Najdanovic
Keyword(s):  
Vector Fields ◽  
Metric Tensor ◽  
The Subject ◽  
Curvature Tensors ◽  
Riemannian Spaces

In this paper we consider concircular vector fields of manifolds with non-symmetric metric tensor. The subject of our paper is an equitorsion concircular mapping. A mapping f : GRN?GRN? is an equitorsion if the torsion tensors of the spaces GRN and GRN? are equal. For an equitorsion concircular mapping of two generalized Riemannian spaces GRN and GRN, we obtain some invariant curvature tensors of this mapping Z?,? = 1,2,... 5, given by equations (3.14, 3.21, 3.28, 3.31, 3.38). These quantities are generalizations of the concircular tensor Z given by equation (2.5).

scholarly journals Generalized φ(Ric)-vector fields in special pseudo-Riemannian spaces

2021 ◽  
Vol 14 (4) ◽  
pp. 1-12
Author(s):  
Nina Vashpanova ◽  
Aleksandr Savchenko ◽  
Nataliia Vasylieva
Keyword(s):  
Vector Fields ◽  
Conformally Flat ◽  
Metric Tensor ◽  
Riemannian Spaces

The paper treats pseudo-Riemannian spaces permitting generalized φ(Ric)-vector fields. We study conditions for the existence of such vector fields in conformally flat, equidistant, reducible and Kählerian pseudo-Riemannian spaces. The obtained results can be applied for the construction of generalized φ(Ric)-vector fields that differ from φ(Ric)-vector fields. The research is carried out locally without limitations imposed on a sign of metric tensor.

scholarly journals Geodesic mappings of quasi-Einstein spaces with a constant scalar curvature

2020 ◽  
Vol 53 (2) ◽  
pp. 212-217 ◽  
Author(s):  
V. A. Kiosak ◽  
G. V. Kovalova
Keyword(s):  
Scalar Curvature ◽  
Linear Form ◽  
Constant Scalar Curvature ◽  
Tensor Form ◽  
Metric Tensor ◽  
Einstein Spaces ◽  
Basic Equations ◽  
Riemannian Spaces

In this paper we study a special type of pseudo-Riemannian spaces - quasi-Einstein spaces of constant scalar curvature. These spaces are generalizations of known Einstein spaces. We obtained a linear form of the basic equations of the theory of geodetic mappings for these spaces. The studies are conducted locally in tensor form, without restrictions on the sign and signature of the metric tensor.

scholarly journals The Dаrbоuх Theory and Geodesics in the Metric Space with Torsion

2020 ◽  
Vol 7 ◽  
Keyword(s):  
Curvature Tensor ◽  
Metric Space ◽  
Jacobi Identity ◽  
Torsion Tensor ◽  
Metric Tensor ◽  
Fundamental Tensor ◽  
Geodesic Lines ◽  
Riemannian Spaces

The geometry of n Yn space is generated congruently together by the metric tensor and the torsion tensor. In the presented article has been obtained an analog of the Dаrbоuх theory in the n Yn space, also studied the deduction of the equation of the geodesic lines on the hypersurface that embedded in such spaces, showed that in the n Yn space the structure of the curvature tensor has special features and for curvature tensor obtained Ricci - Jacobi identity. We establish that the equations of the geodesics have additional summands, which are caused by the presence of torsion in the space. In n Yn space, the variation of the length of the geodesic lines is proportional to the product of metric and torsion tensors gijSjpk. We have introduced the second fundamental tensor παβ for the hypersurface n Yn-1 and established its structure, which is fundamentally different from the case of the Riemannian spaces with zero torsion. Furthermore, the results on the structure of the curvature tensor have been obtained.

ON THE GEOMETRY OF GRADED CONSTRAINT ALGEBRAS: VIELBEINS, METRIC TENSORS AND THE STRING VERTEX SUPEROPERATORS

1989 ◽  
Vol 04 (17) ◽  
pp. 1667-1679
Author(s):  
HENRIK ARATYN
Keyword(s):  
Virasoro Algebra ◽  
Geometric Interpretation ◽  
Geometric Construction ◽  
Canonical Mapping ◽  
Metric Tensor ◽  
Constraint Algebra ◽  
Metric Tensors

The geometric interpretation of the vertex superoperators in the Neveu-Schwarz-Ramond (NSR) model is provided by associating them with a canonical mapping between abelian operators and generators of the super-Virasoro algebra. In this setting, the moments of the vertex superoperators are the corresponding vielbiens carrying graded indices. This geometric construction defines a natural metric tensor associated with the graded constraint algebra. Consequently, our approach yields the simple Batalin-Fradkin-Vilkovisky Hamiltonian for the NSR model as the “square” of a graded vector, manifestly invariant under OSP (1, 1|2).

Indefinite Finsler Spaces and Timelike Spaces

1970 ◽  
Vol 22 (5) ◽  
pp. 1035-1039 ◽  
Author(s):  
John K. Beem
Keyword(s):  
Triangle Inequality ◽  
Finsler Space ◽  
Sufficient Conditions ◽  
Partial Ordering ◽  
Two Dimensional ◽  
Finsler Spaces ◽  
Metric Tensor ◽  
Timelike Surface ◽  
Lorentz Manifolds ◽  
Riemannian Spaces

In this paper we investigate indefinite Finsler spaces in which the metric tensor has signature n — 2. These spaces are a generalization of Lorentz manifolds. Locally a partial ordering may be defined such that the reverse triangle inequality holds for this partial ordering. Consequently, the spaces we study may be made into what Busemann [3] terms locally timelike spaces. Furthermore, sufficient conditions are obtained for an indefinite Finsler space to be a doubly timelike surface (see [2; 4]). In particular, all two-dimensional pseudo-Riemannian spaces are shown to be doubly timelike surfaces.

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