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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2024.5
- 수록면
- 867 - 873 (7page)
- DOI
- 10.4134/BKMS.b230497
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초록· 키워드
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A pseudo-Riemannian solvmanifold is a solvable Lie group endowed with a left invariant pseudo-Riemannian metric. In this short note, we investigate the nilpotency of the Ricci operator of pseudo-Rie\-mannian solvmanifolds. We focus on a special class of solvable Lie groups whose Lie algebras can be expressed as a one-dimensional extension of a nilpotent Lie algebra $\mathbb{R}D\ltimes \mathfrak{n}$, where $D$ is a derivation of $\mathfrak{n}$ whose restriction to the center of $\mathfrak{n}$ has at least one real eigenvalue. The main result asserts that every solvable Lie group belonging to this special class admits a left invariant pseudo-Riemannian metric with nilpotent Ricci operator. As an application, we obtain a complete classification of three-dimensional solvable Lie groups which admit a left invariant pseudo-Riemannian metric with nilpotent Ricci operator.
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