In this paper, using special metric deformations introduced by Aubin, we construct Riemannian metrics satisfying non-vanishing conditions concerning the Weyl tensor, on every compact manifold. In particular, in dimension four, we show that there are no topological obstructions for the existence of metrics with non-vanishing Bach tensor.
Some canonical metrics via Aubin's local deformations / G. Catino, D. Dameno, P. Mastrolia. - In: JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES. - ISSN 0021-7824. - 191:(2024 Nov), pp. 103624.1-103624.25. [10.1016/j.matpur.2024.103624]
Some canonical metrics via Aubin's local deformations
D. DamenoPenultimo
;P. Mastrolia
Ultimo
2024
Abstract
In this paper, using special metric deformations introduced by Aubin, we construct Riemannian metrics satisfying non-vanishing conditions concerning the Weyl tensor, on every compact manifold. In particular, in dimension four, we show that there are no topological obstructions for the existence of metrics with non-vanishing Bach tensor.
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