Schouten like metrics on five dimensional nilpotents Lie groups

Marius Landry Foka; Michel Bertrand Ngaha Djiadeu; Thomas Bouetou Bouetou

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arXiv · 2412.20000

Schouten like metrics on five dimensional nilpotents Lie groups

Marius Landry Foka·Michel Bertrand Ngaha Djiadeu·Thomas Bouetou Bouetou

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Abstract

The prescribed Ricci curvature problem involves finding a Riemannian metric g that satisfies the equation ric(g) = T, where T is a fixed symmetric (0, 2)-tensor field on a differential manifold M. In this paper, we introduce the concept of Schouten-like metrics as particular solutions to the prescribed Ricci curvature problem. We classify these metrics on five-dimensional nilpotent Lie groups by establishing a connection with algebraic Schouten solitons. This approach also enables us to classify five-dimensional nilsolitons, providing a comprehensive understanding of their geometric structures and properties.

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BibTeX RIS

Marius Landry Foka, Michel Bertrand Ngaha Djiadeu, Thomas Bouetou Bouetou. 2025-05-27. Schouten like metrics on five dimensional nilpotents Lie groups. https://arxiv.org/abs/2412.20000

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