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Search Results (4)

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Keywords = Kobayashi–Nomizu connections

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19 pages, 294 KiB  
Article
Classification of Algebraic Schouten Solitons on Lorentzian Lie Groups Associated with the Perturbed Canonical Connection and the Perturbed Kobayashi–Nomizu Connection
by Jinguo Jiang and Yanni Yang
Symmetry 2025, 17(1), 10; https://doi.org/10.3390/sym17010010 - 25 Dec 2024
Viewed by 540
Abstract
In this paper, we investigate the algebraic conditions of algebraic Schouten solitons on three-dimensional Lorentzian Lie groups associated with the perturbed canonical connection and the perturbed Kobayashi–Nomizu connection. Furthermore, we provide the complete classification for these algebraic Schouten solitons on three-dimensional Lorentzian Lie [...] Read more.
In this paper, we investigate the algebraic conditions of algebraic Schouten solitons on three-dimensional Lorentzian Lie groups associated with the perturbed canonical connection and the perturbed Kobayashi–Nomizu connection. Furthermore, we provide the complete classification for these algebraic Schouten solitons on three-dimensional Lorentzian Lie groups associated with the algebraic Schouten solitons. The main results indicate that G4 does not possess algebraic Schouten solitons related to the perturbed Kobayashi–Nomizu connection, G1,G2,G3,G6, and G7 possess algebraic Schouten solitons, and the result for G5 is trivial. Full article
(This article belongs to the Section Mathematics)
18 pages, 323 KiB  
Article
On the Geometry of Kobayashi–Nomizu Type and Yano Type Connections on the Tangent Bundle with Sasaki Metric
by Esmaeil Peyghan, Davood Seifipour and Ion Mihai
Mathematics 2023, 11(18), 3865; https://doi.org/10.3390/math11183865 - 10 Sep 2023
Viewed by 1385
Abstract
In this paper, we address the study of the Kobayashi–Nomizu type and the Yano type connections on the tangent bundle TM equipped with the Sasaki metric. Then, we determine the curvature tensors of these connections. Moreover, we find conditions under which these [...] Read more.
In this paper, we address the study of the Kobayashi–Nomizu type and the Yano type connections on the tangent bundle TM equipped with the Sasaki metric. Then, we determine the curvature tensors of these connections. Moreover, we find conditions under which these connections are torsion-free, Codazzi, and statistical structures, respectively, with respect to the Sasaki metric. Finally, we introduce the mutual curvature tensor on a manifold. We investigate some of its properties; furthermore, we study mutual curvature tensors on a manifold equipped with the Kobayashi–Nomizu type and the Yano type connections. Full article
18 pages, 773 KiB  
Article
Algebraic Schouten Solitons of Three-Dimensional Lorentzian Lie Groups
by Siyao Liu
Symmetry 2023, 15(4), 866; https://doi.org/10.3390/sym15040866 - 5 Apr 2023
Cited by 2 | Viewed by 1302
Abstract
In 2016, Wears defined and studied algebraic T-solitons. In this paper, we define algebraic Schouten solitons as a special T-soliton and classify the algebraic Schouten solitons associated with Levi-Civita connections, canonical connections, and Kobayashi–Nomizu connections on three-dimensional Lorentzian Lie groups that have some [...] Read more.
In 2016, Wears defined and studied algebraic T-solitons. In this paper, we define algebraic Schouten solitons as a special T-soliton and classify the algebraic Schouten solitons associated with Levi-Civita connections, canonical connections, and Kobayashi–Nomizu connections on three-dimensional Lorentzian Lie groups that have some product structure. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry: Differential Geometry and Its Applications)
31 pages, 312 KiB  
Article
Codazzi Tensors and the Quasi-Statistical Structure Associated with Affine Connections on Three-Dimensional Lorentzian Lie Groups
by Tong Wu and Yong Wang
Symmetry 2021, 13(8), 1459; https://doi.org/10.3390/sym13081459 - 9 Aug 2021
Cited by 3 | Viewed by 1768
Abstract
In this paper, we classify three-dimensional Lorentzian Lie groups on which Ricci tensors associated with Bott connections, canonical connections and Kobayashi–Nomizu connections are Codazzi tensors associated with these connections. We also classify three-dimensional Lorentzian Lie groups with the quasi-statistical structure associated with Bott [...] Read more.
In this paper, we classify three-dimensional Lorentzian Lie groups on which Ricci tensors associated with Bott connections, canonical connections and Kobayashi–Nomizu connections are Codazzi tensors associated with these connections. We also classify three-dimensional Lorentzian Lie groups with the quasi-statistical structure associated with Bott connections, canonical connections and Kobayashi–Nomizu connections. Full article
(This article belongs to the Section Mathematics)
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