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IPHP transformations on tangent bundle of a Riemannian manifold with respect to a class of lift metrics
M. Zohrehvand Department of Mathematical Sciences and Statistics,
Malayer University,
Malayer, Iran
Аннотация:
Let $(M_n, g)$ be an $n$-dimensional Riemannian manifold and $TM_n$ its tangent bundle. In this article, we study the infinitesimal paraholomorphically projective (IPHP) transformations on $TM_n$ with respect to the Levi-Civita connection of the pseudo-Riemannian metric $\tilde{g}=\alpha g^S+\beta g^C+\gamma g^V$, where $\alpha$, $\beta$ and $\gamma$ are real constants with $\alpha(\alpha+\gamma)-\beta^2\ne0$ and $g^S$, $g^C$ and $g^V$ are diagonal lift, complete lift and vertical lift of $g$, respectively. We determine this type of transformations and then prove that if $(TM_n,\tilde{g})$ has a non-affine infinitesimal paraholomorphically projective transformation, then $M_n$ and $TM_n$ are locally flat.
Ключевые слова и фразы:
$g$-natural metrics, infinitesimal paraholomorphically projective transformations, adapted almost paracomplex structure.
Поступила в редакцию: 20.03.2019
Образец цитирования:
M. Zohrehvand, “IPHP transformations on tangent bundle of a Riemannian manifold with respect to a class of lift metrics”, Eurasian Math. J., 13:2 (2022), 82–92
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/emj441 https://www.mathnet.ru/rus/emj/v13/i2/p82
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Страница аннотации: | 67 | PDF полного текста: | 38 | Список литературы: | 2 |
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