Semi-Symmetric Curvature Properties of Robertson–Walker Spacetimes
DOI:
https://doi.org/10.15407/mag18.03.368Ключові слова:
лоренцевий многовид, симетричний простор, простiр-час Робертсона–Вокера, узагальнений простiр-час Робертсона–Вокера, простiр-час iдеальної рiдини, простiр-час квазiсталої кривини, тензори проективної та конформної кривиниАнотація
Метою цiєї роботи є характеризацiя просторiв-часiв Робертсона–Вокера (РВ), що задовольняють деякi умови на кривину. Отримано необхiднi та достатнi умови того, що РВ простiр-час є Рiччi напiвсиметричним. Доведено, що чотиривимiрний Рiччi симетричний РВ простiр-час є вакуумним. Також ми дослiджуємо властивостi проективної колiнеацiї та колiнеацiї матерiї в рамках чотиривимiрного Рiччi симетричного РВ простору-часу. Помiж iншого доведено, що лоренцевий многовид розмiрностi n ≥ 3 є РВ простором тодi, i лише тодi, коли простiр-час має квазiсталу кривину. Нарештi, отримано деякi новi характеристики РВ просторiв-часiв.
Mathematical Subject Classification 2010: 53B30, 53B50, 53C15
Посилання
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