Properties of Modified Riemannian Extensions
Let M be an n-dimensional differentiable manifold with a symmetric connection ∇ and T*M be its cotangent bundle. In this paper, we study some properties of the modified Riemannian extension ğ∇, c on T*M defined by means of a symmetric (0, 2)-tensor field c on M. We get the conditions under which T*M...
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| Date: | 2015 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | English |
| Published: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2015
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| Series: | Журнал математической физики, анализа, геометрии |
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/118024 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Properties of Modified Riemannian Extensions / A. Gezer, L. Bilen, A. Cakmak // Журнал математической физики, анализа, геометрии. — 2015. — Т. 11, № 2. — С. 159-173. — Бібліогр.: 24 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | Let M be an n-dimensional differentiable manifold with a symmetric connection ∇ and T*M be its cotangent bundle. In this paper, we study some properties of the modified Riemannian extension ğ∇, c on T*M defined by means of a symmetric (0, 2)-tensor field c on M. We get the conditions under which T*M endowed with the horizontal lift HJ of an almost complex structure J and with the metric ğ∇, c is a Kähler-Norden manifold. Also curvature properties of the Levi-Civita connection of the metric ğ∇, c are presented. |
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