Congruences Of Null Strings Research Articles

Hyperheavenly spaces and their application in Walker and para-Kähler geometries: Part II

4-dimensional spaces equipped with congruences of null strings are considered. It is assumed that a space admits a congruence of expanding self-dual null strings and its self-dual part of the Weyl tensor is algebraically degenerate. Different Petrov-Penrose types of such spaces are analyzed. A special attention is paid to para-Kähler Einstein spaces. All para-Kähler Einstein metrics of spaces with algebraically degenerate self-dual Weyl spinor are found in all the generality.

Hyperheavenly spaces and their application in Walker and para-Kähler geometries: Part I

Spaces equipped with congruences of null strings are considered. A special attention is paid to the spaces which belong to the two-sided Walker class and para-Kähler class. Properties of an intersection of self-dual and anti-self-dual congruences of null strings are used as an additional criterion for a classification of such spaces. Finally, a few examples of para-Kähler and para-Kähler-Einstein spaces are presented.

Congruences of Null Strings and Their Relations with Weyl Tensor and Traceless Ricci Tensor

Congruences of Null Strings and Their Relations with Weyl Tensor and Traceless Ricci Tensor

Nonexpanding congruences of null strings in algebraically degenerate right-flat spaces

A problem of nonexpanding right congruences of null strings in algebraically degenerate right-flat spaces is discussed and reduced to one differential equation. Then the form of the “key” function from the right side for some subclass of metrics is studied.