scholarly journals Geodesic mappings of compact quasi-Einstein spaces, I

2020 ◽  
Vol 13 (1) ◽  
pp. 35-48 ◽  
Author(s):  
Volodymyr Kiosak ◽  
Aleksandr Savchenko ◽  
Galina Kovalova
Keyword(s):  
Main Type ◽  
Einstein Spaces ◽  
Riemannian Spaces

The paper treats a particular type of pseudo-Riemannian spaces, namely quasi-Einstein spaces with gradient dening vector. These spaces are a generalization of well-known Einstein spaces. There are three types of these spaces that permit locally geodesic mappings. Authors proved "a theorem of disappearance" for compact quasi-Einstein spaces of main type.

scholarly journals On conformally reducible pseudo-Riemannian spaces

2021 ◽  
Vol 14 (2) ◽  
pp. 154-163
Author(s):  
Тетяна Iванiвна Шевченко ◽  
Тетяна Сергіївна Спічак ◽  
Дмитро Миколайович Дойков
Keyword(s):  
General Theory ◽  
Conformal Mapping ◽  
Main Type ◽  
Complete Classification ◽  
Riemann Tensor ◽  
Conformally Flat ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
Einstein Spaces

The present paper studies the main type of conformal reducible conformally flat spaces. We prove that these spaces are subprojective spaces of Kagan, while Riemann tensor is defined by a vector defining the conformal mapping. This allows to carry out the complete classification of these spaces. The obtained results can be effectively applied in further research in mechanics, geometry, and general theory of relativity. Under certain conditions the obtained equations describe the state of an ideal fluid and represent quasi-Einstein spaces. Research is carried out locally in tensor shape.

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 Геодезичні відображення коспактних квазі-ейнштейнових просторів

2021 ◽  
Vol 14 (1) ◽  
pp. 80-91
Author(s):  
Володимир Анатолійович Кіосак ◽  
Александр Савченко ◽  
Олександр Латиш
Keyword(s):  
Symmetric Spaces ◽  
Main Type ◽  
Einstein Spaces

The paper treats geodesic mappings of quasi-Einstein spaces with gradient defining vector. Previously the authors defined three types of these spaces. In the present paper it is proved that there are no quasi-Einstein spaces of special type. It is demonstrated that quasi-Einstein spaces of main type are closed with respect to geodesic mappings. The spaces of particular type are proved to be geodesic $D$-symmetric spaces.  

The mobility of Riemannian spaces with respect to conformal mappings onto Einstein spaces

2010 ◽  
Vol 54 (8) ◽  
pp. 29-33 ◽  
Author(s):  
L. E. Evtushik ◽  
V.A. Kiosak ◽  
J. Mikeš
Keyword(s):  
Conformal Mappings ◽  
Einstein Spaces ◽  
Riemannian Spaces

scholarly journals Einstein spaces of class one

1937 ◽  
Vol 43 (4) ◽  
pp. 265-271
Author(s):  
C. B. Allendoerfer
Keyword(s):  
Einstein Spaces

A Series of Terracottas representing Artemis, found at Tarentum

1927 ◽  
Vol 47 (1) ◽  
pp. 93-101 ◽  
Author(s):  
D. B. Harden
Keyword(s):  
Main Type ◽  
Large Group ◽  
The Many

Among the many thousands of terracottas recently recovered from the soil at Tarentum, there is one large group which has not yet received much mention in print. I refer to a series of some hundreds of female statuettes which have been identified by Duemmler and Winter as Artemis figures. The majority of these figures are at present in the Museo Nazionale at Taranto, though some few have found their way into museums elsewhere.In the main type of the figures there is little variation. They usually range from eight to twelve inches in height, and are standing, female, draped figures each with one or more attributes. They all wear either a lion-skin head-dress, or a lion-skin apron; some, indeed, show both the head-dress and the apron. Most of the examples are single-moulded statuettes with unmodelled back, but there are a few which are almost reliefs. The figurines are for the most part rough and not retouched after moulding, though there are some finely modelled exceptions to this rule.

Einstein spaces which are mapped conformally on each other

1925 ◽  
Vol 94 (1) ◽  
pp. 119-145 ◽  
Author(s):  
H. W. Brinkmann
Keyword(s):  
Einstein Spaces

Composite Сarbonaceous Сoal-Water Suspensions

2021 ◽  
Vol 1045 ◽  
pp. 212-225
Author(s):  
Olena Svietkina ◽  
Kostiantyn Bas ◽  
Sergiy Boruk ◽  
Roman Klishchenko ◽  
Oleksandr Yehurnov ◽  
...  
Keyword(s):  
Power Plants ◽  
Statistical Data ◽  
Main Type ◽  
Thermal Power ◽  
Electric Energy ◽  
Oil Refining ◽  
Thermal Power Plants ◽  
Water Suspensions ◽  
Ash And Slag Waste ◽  
Slag Waste

In Ukraine, up to 75% of all electricity is supplied by thermal power plants, the main type of fuel for which is coal, which leads to the release of ash and slag waste at power plants in huge quantities. Every 10 years (according to statistical data) the amount of ash and slag produced at thermal power plants doubles. The use and creation of new modified consumers of coal-water fuel (CWF) and coal-water suspensions (CWS) occurs periodically. The ease of handling suspensions is captivating: in the energy sector, they can serve as the basis for the effective disposal of numerous accumulated wastes from coal preparation and oil refining, a significant reduction in the consumption of minerals for generating heat and electric energy, and minimizing the effect of heat power engineering on public health and the state of nature.

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