Codazzi tensor fields in reductive homogeneous spaces
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909090472525824 |
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| author | Reber, James Marshall Terek, Ivo |
| author_facet | Reber, James Marshall Terek, Ivo |
| contents | We extend the results about left-invariant Codazzi tensor fields on Lie groups equipped with left-invariant Riemannian metrics obtained by d'Atri in 1985 to the setting of reductive homogeneous spaces $G/H$, where the curvature of the canonical connection of second kind associated with the fixed reductive decomposition $\mathfrak{g} = \mathfrak{h}\oplus\mathfrak{m}$ enters the picture. In particular, we show that invariant Codazzi tensor fields on a naturally reductive homogeneous space are parallel. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_07444 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Codazzi tensor fields in reductive homogeneous spaces Reber, James Marshall Terek, Ivo Differential Geometry 53C30 We extend the results about left-invariant Codazzi tensor fields on Lie groups equipped with left-invariant Riemannian metrics obtained by d'Atri in 1985 to the setting of reductive homogeneous spaces $G/H$, where the curvature of the canonical connection of second kind associated with the fixed reductive decomposition $\mathfrak{g} = \mathfrak{h}\oplus\mathfrak{m}$ enters the picture. In particular, we show that invariant Codazzi tensor fields on a naturally reductive homogeneous space are parallel. |
| title | Codazzi tensor fields in reductive homogeneous spaces |
| topic | Differential Geometry 53C30 |
| url | https://arxiv.org/abs/2306.07444 |