Тензор Коттона

В дифференциальной геометрии тензор Коттона на (псевдо)-римановом многообразии размерности n задаётся как тензор 3-го ранга, определяемый с помощью метрики.

Назван в честь Эмиля Коттона.

Определение

Тензор Коттона можно записать в координатах следующим образом

где тензор Риччи и скалярная кривизна

Про Тензор Коттона можно думать как про векторно-значную 2-форму.

Свойства

  • Равенство нулю тензора Коттона для размерности является необходимым и достаточным условием того, что многообразие является конформно евклидовым.
    • В размерностях аналогичным свойством обладает тензору Вейля.

Литература

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