Differential Properties of Mappings with Bounded Distortion and Conformal Mappings of Riemannian Spaces

1994 ◽  
pp. 356-382
Author(s):  
Yu. G. Reshetnyak
Keyword(s):  
Conformal Mappings ◽  
Bounded Distortion ◽  
Differential Properties ◽  
Riemannian Spaces

scholarly journals Conformal and Geodesic Mappings onto Some Special Spaces

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 664 ◽  
Author(s):  
Volodymyr Berezovski ◽  
Yevhen Cherevko ◽  
Lenka Rýparová
Keyword(s):  
Differential Equations ◽  
Closed System ◽  
Symmetric Spaces ◽  
Conformal Mappings ◽  
Cauchy Type ◽  
Affine Connections ◽  
Covariant Derivatives ◽  
Riemannian Spaces

In this paper, we consider conformal mappings of Riemannian spaces onto Ricci-2-symmetric Riemannian spaces and geodesic mappings of spaces with affine connections onto Ricci-2-symmetric spaces. The main equations for the mappings are obtained as a closed system of Cauchy-type differential equations in covariant derivatives. We find the number of essential parameters which the solution of the system depends on. A similar approach was applied for the case of conformal mappings of Riemannian spaces onto Ricci-m-symmetric Riemannian spaces, as well as geodesic mappings of spaces with affine connections onto Ricci-m-symmetric spaces.

Conformal Mappings of Riemannian Spaces onto Ricci Symmetric Spaces

2018 ◽  
Vol 103 (1-2) ◽  
pp. 304-307 ◽  
Author(s):  
V. E. Berezovskii ◽  
I. Hinterleitner ◽  
N. I. Guseva ◽  
J. Mikeš
Keyword(s):  
Symmetric Spaces ◽  
Conformal Mappings ◽  
Riemannian 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

Quantum Anomalies via Differential Properties of Lebesgue–Feynman Generalized Measures

2020 ◽  
Vol 310 (1) ◽  
pp. 98-107
Author(s):  
John E. Gough ◽  
Tudor S. Ratiu ◽  
Oleg G. Smolyanov
Keyword(s):  
Quantum Anomalies ◽  
Differential Properties

Large-scale bounded distortion mappings

2015 ◽  
Vol 34 (6) ◽  
pp. 1-10 ◽  
Author(s):  
Shahar Z. Kovalsky ◽  
Noam Aigerman ◽  
Ronen Basri ◽  
Yaron Lipman
Keyword(s):  
Large Scale ◽  
Bounded Distortion

scholarly journals Proposals on calculating the differential properties of concrete

2021 ◽  
Vol 1083 (1) ◽  
pp. 012009
Author(s):  
L R Mailyan ◽  
S A Stel‘makh ◽  
E M Shcherban‘ ◽  
A P Korobkin ◽  
E A Efimenko
Keyword(s):  
Differential Properties

The Curvature Theory of Line Trajectories in Spatial Kinematics

1981 ◽  
Vol 103 (4) ◽  
pp. 718-724 ◽  
Author(s):  
J. M. McCarthy ◽  
B. Roth
Keyword(s):  
Planar Motion ◽  
Spatial Motion ◽  
Third Order ◽  
Local Shape ◽  
The Third ◽  
Moving Body ◽  
Physical Representation ◽  
Curvature Theory ◽  
Spatial Kinematics ◽  
Differential Properties

This paper develops the differential properties of ruled surfaces in a form which is applicable to spatial kinematics. Derivations are presented for the three curvature parameters which define the local shape of a ruled surface. Related parameters are also developed which allow a physical representation of this shape as generated by a cylindric-cylindric crank. These curvature parameters are then used to define all the lines in the moving body which instantaneously generate speciality shaped trajectories. Such lines may be used in the synthesis of spatial motions in the same way that the points on the inflection circle and cubic of stationary curvature are used to synthesize planar motion. As an example of this application several special sets of lines are defined: the locus of all lines which for a general spatial motion instantaneously generate helicoids to the second order and the locus of lines generating right hyperboloids to the third order.

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