The antecedent of Einstein field equations with Euclidean signature is the complex elliptic Monge-Ampère equation, CMA2. For elliptic CMA2 solutions determine hyper-Kähler, self-dual and therefore Ricci-flat metrics with Euclidean signature. We shall consider a symmetry reduction of CMA2 to solutions that admit only a single Killing vector. Systematic studies of vacuum metrics with one Killing ...

Abstract In the recent paper by one of the authors (MBS) and A. Malykh on the classification of second-order PDEs with four independent variables that possess partner symmetries [1], mixed heavenly equation appears as one of the canonical equations admitting partner symmetries. Here for the mixed heavenly equation, formulated in a two-component form, we present a Lax pair of Olver-Ibragimov-Sha...

In the recent paper by one of the authors (MBS) and A. A. Malykh on the classification of second-order PDEs with four independent variables that possess partner symmetries [1], mixed heavenly equation and Husain’s equation appear as closely related canonical equations admitting partner symmetries. Here for the mixed heavenly equation and Husain’s equation, formulated in a two-component form, we...

This is a truly essential aspect of your study because writing it forces you to clarify and crystallize to yourself as well as to readers what is the core point of your investigation. In some cases people who evaluate your research proposal only read the abstract; because of that it need to be truly convincing and thoroughly understandable without reading the rest of the research proposal. Avoi...

Peter Jackson's Heavenly Creatures (1994) is the story of two girls in New Zealand who form an intense erotic friendship based on a fantasy world they create, and how their forced separation leads them to commit matricide. Beneath the sensational surface, though, is another story: this is a film about cinema, about desire, and how queer spectators create new and unexpected meanings. This articl...

I herewith affirm that I completed the work myself, and did not use any other than the mentioned sources and utilities. Acknowledgements II Acknowledgements Firstly I would like to thank my parents Gabriele M. König and Anthony D. Wright as well as other family members for their continued support and guidance not only with respect to my work but also with respect to day to day situations. I val...