A lorentz manifold with a group of conformal transformations possessing a normal one-parameter subgroup of homotheties

1997 ◽  
Vol 38 (6) ◽  
pp. 1178-1181
Author(s):  
M. N. Podoksënov
Keyword(s):  
Lorentz Manifold ◽  
Conformal Transformations

scholarly journals Conformal mapping of the Misner–Sharp mass from gravitational collapse

2016 ◽  
Vol 25 (07) ◽  
pp. 1650081 ◽  
Author(s):  
Fayçal Hammad
Keyword(s):  
Conformal Mapping ◽  
Gravitational Collapse ◽  
Conformal Transformation ◽  
Conformal Mappings ◽  
Conformal Transformations ◽  
Theories Of Gravity ◽  
Definition Of ◽  
Geometric Definition

The conformal transformation of the Misner–Sharp mass is reexamined. It has recently been found that this mass does not transform like usual masses do under conformal mappings of spacetime. We show that when it comes to conformal transformations, the widely used geometric definition of the Misner–Sharp mass is fundamentally different from the original conception of the latter. Indeed, when working within the full hydrodynamic setup that gave rise to that mass, i.e. the physics of gravitational collapse, the familiar conformal transformation of a usual mass is recovered. The case of scalar–tensor theories of gravity is also examined.

scholarly journals The Scalar Curvature of a Riemannian Almost Paracomplex Manifold and Its Conformal Transformations

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1379
Author(s):  
Vladimir Rovenski ◽  
Josef Mikeš ◽  
Sergey Stepanov
Keyword(s):  
Riemannian Manifold ◽  
Scalar Curvature ◽  
Conformal Transformations ◽  
Structural Group

A Riemannian almost paracomplex manifold is a 2n-dimensional Riemannian manifold (M,g), whose structural group O(2n,R) is reduced to the form O(n,R)×O(n,R). We define the scalar curvature π of this manifold and consider relationships between π and the scalar curvature s of the metric g and its conformal transformations.

Problems of Plane Elasticity for Reinforced Boundaries

1955 ◽  
Vol 22 (2) ◽  
pp. 249-254
Author(s):  
J. R. M. Radok
Keyword(s):  
Plane Elasticity ◽  
Conformal Transformations ◽  
Thin Sheets ◽  
General Method

Abstract Based on N. I. Muskhelishvili’s approach to problems of plane elasticity, a general method has been deduced for the solution of problems of reinforced cutouts in infinitely thin sheets. As an illustration, the circular reinforced hole has been treated in detail and the results have been related to those obtained experimentally and theoretically by other authors. The solution for other shapes of cutouts will be greatly simplified, since full use may be made of the theory of conformal transformations.

Power-law inflation and conformal transformations

1994 ◽  
Vol 11 (2) ◽  
pp. 383-387 ◽  
Author(s):  
Spiros Cotsakis ◽  
Paul J Saich
Keyword(s):  
Power Law ◽  
Conformal Transformations
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