scholarly journals Rotary mappings of spaces with affine connection

Filomat ◽  
2019 ◽  
Vol 33 (4) ◽  
pp. 1147-1152
Author(s):  
Josef Mikes ◽  
Lenka Rýparová
Keyword(s):  
Riemannian Space ◽  
Affine Connection ◽  
Two Dimensional ◽  
Riemannian Spaces

This paper concerns with rotary mappings of two-dimensional spaces with an affine connection onto (pseudo-) Riemannian spaces. The results obtained in the theory of rotary mappings are further developed. We prove that any (pseudo-) Riemannian space admits rotary mapping. There are also presented certain properties from which yields the existence of these rotary mappings.

VIII.—Riemann Extensions which have Kähler Metrics.

1954 ◽  
Vol 64 (2) ◽  
pp. 113-126 ◽  
Author(s):  
E. M. Patterson
Keyword(s):  
Riemannian Space ◽  
Affine Connection ◽  
Sufficient Conditions ◽  
Projective Spaces ◽  
Necessary And Sufficient Conditions ◽  
Canonical Forms ◽  
Complex Manifolds ◽  
Necessary And Sufficient ◽  
Riemann Extension ◽  
Riemannian Spaces

SynopsisCertain types of 2n-dimensional Riemannian spaces admitting parallel fields of null n-planes are studied. These are known as Riemann extensions of conformal, projective or other classes of spaces of affine connection. The circumstances under which a 2n-dimensional Riemannian space admits two non-intersecting parallel fields of null n-planes are also discussed. Such spaces satisfy a condition similar to Kähler's condition in the theory of complex manifolds, and hence are called Kähler spaces. Necessary and sufficient conditions are found for a Kähler space to be a Riemann extension with respect to one of the parallel fields of null n-planes, and canonical forms are found for the metrics in the cases of Riemann extensions of conformal and projective spaces.

scholarly journals Infinitesimal rotary transformation

Filomat ◽  
2019 ◽  
Vol 33 (4) ◽  
pp. 1153-1157
Author(s):  
Lenka Rýparová ◽  
Josef Mikes
Keyword(s):  
Riemannian Space ◽  
Basic Equations ◽  
Fundamental Equations ◽  
Principal Parts ◽  
Infinitesimal Transformations ◽  
Riemannian Spaces

The paper is devoted to further study of a certain type of infinitesimal transformations of twodimensional (pseudo-) Riemannian spaces, which are called rotary. Aninfinitesimal transformation is called rotary if it maps any geodesic on (pseudo-) Riemannian space onto an isoperimetric extremal of rotation in their principal parts on (pseudo-) Riemannian space. We study basic equations of the infinitesimal rotary transformations in detail and obtain the simpler fundamental equations of these transformations.

scholarly journals Some invariants of conformal mappings of a generalized Riemannian space

Filomat ◽  
2018 ◽  
Vol 32 (4) ◽  
pp. 1465-1474
Author(s):  
Nenad Vesic
Keyword(s):  
Curvature Tensor ◽  
Riemannian Space ◽  
Affine Connection ◽  
Conformal Mappings ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Conformal Curvature ◽  
Conformal Curvature Tensor ◽  
Necessary And Sufficient ◽  
Weyl Conformal Curvature Tensor

Invariants of conformal mappings between non-symmetric affine connection spaces are obtained in this paper. Correlations between these invariants and the Weyl conformal curvature tensor are established. Before these invariants, it is obtained a necessary and sufficient condition for a mapping to be conformal. Some appurtenant invariants of conformal mappings are obtained.

TWO-LOOP BETA-FUNCTION FOR NONLINEAR SIGMA-MODEL WITH AFFINE METRIC MANIFOLD

1994 ◽  
Vol 09 (26) ◽  
pp. 2411-2419 ◽  
Author(s):  
VASILY E. TARASOV
Keyword(s):  
Riemannian Manifolds ◽  
Sigma Model ◽  
Beta Function ◽  
Affine Connection ◽  
Dissipative System ◽  
Nonlinear Sigma Model ◽  
Two Dimensional ◽  
Invariance Condition ◽  
Target Manifold ◽  
Affine Metric

Two-loop metric counterterms for nonlinear two-dimensional bosonic σ-model with affine metric target manifold are calculated. The correlation of the metric and affine connection is derived from conformal invariance condition for nonlinear σ-model which is considered as a dissipative system. Examples of non-flat non-Riemannian manifolds resulting in trivial metric beta-function are suggested.

scholarly journals Cosmological meaning of geometric curvatures

Filomat ◽  
2020 ◽  
Vol 34 (12) ◽  
pp. 4107-4121
Author(s):  
Nenad Vesic
Keyword(s):  
Energy Density ◽  
Physical Meaning ◽  
Riemannian Space ◽  
Energy Momentum Tensor ◽  
State Parameter ◽  
Momentum Tensor ◽  
The State ◽  
Generalized Riemannian Space ◽  
Riemannian Spaces

In this paper, we analyzed the physical meaning of scalar curvatures for a generalized Riemannian space. It is developed the Madsen?s formulae for pressures and energy-densities with respect to the corresponding energy-momentum tensors. After that, the energy-momentum tensors, pressures, energy-densities and state-parameters are analyzed with respect to different concepts of generalized Riemannian spaces. At the end of this paper, linearities of the energy-momentum tensor, pressure, energy-density and the state-parameter are examined.

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