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Search Results (3)

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Keywords = almost co-Kähler manifolds

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12 pages, 766 KiB  
Article
Quarter-Symmetric Metric Connection on a Cosymplectic Manifold
by Miroslav D. Maksimović and Milan Lj. Zlatanović
Mathematics 2023, 11(9), 2209; https://doi.org/10.3390/math11092209 - 8 May 2023
Cited by 1 | Viewed by 1705
Abstract
We study the quarter-symmetric metric A-connection on a cosymplectic manifold. Observing linearly independent curvature tensors with respect to the quarter-symmetric metric A-connection, we construct the Weyl projective curvature tensor on a cosymplectic manifold. In this way, we obtain new conditions for [...] Read more.
We study the quarter-symmetric metric A-connection on a cosymplectic manifold. Observing linearly independent curvature tensors with respect to the quarter-symmetric metric A-connection, we construct the Weyl projective curvature tensor on a cosymplectic manifold. In this way, we obtain new conditions for the manifold to be projectively flat. At the end of the paper, we define η-Einstein cosymplectic manifolds of the θ-th kind and prove that they coincide with the η-Einstein cosymplectic manifold. Full article
(This article belongs to the Special Issue Differential Geometry: Structures on Manifolds and Submanifolds)
20 pages, 309 KiB  
Article
From Dual Connections to Almost Contact Structures
by Emmanuel Gnandi and Stéphane Puechmorel
Mathematics 2022, 10(20), 3822; https://doi.org/10.3390/math10203822 - 16 Oct 2022
Viewed by 1982
Abstract
A dualistic structure on a smooth Riemaniann manifold M is a triple (M,g,∇) with g a Riemaniann metric and ∇ an affine connection generally assumed to be torsionless. From g and ∇, dual connection ∇* can [...] Read more.
A dualistic structure on a smooth Riemaniann manifold M is a triple (M,g,∇) with g a Riemaniann metric and ∇ an affine connection generally assumed to be torsionless. From g and ∇, dual connection ∇* can be defined. In this work, we give conditions on the basis of this notion for a manifold to admit an almost contact structure and some related structures: almost contact metric, contact, contact metric, cosymplectic, and co-Kähler in the three-dimensional case. Full article
(This article belongs to the Special Issue Complex and Contact Manifolds II)
11 pages, 291 KiB  
Article
η-∗-Ricci Solitons and Almost co-Kähler Manifolds
by Arpan Sardar, Mohammad Nazrul Islam Khan and Uday Chand De
Mathematics 2021, 9(24), 3200; https://doi.org/10.3390/math9243200 - 11 Dec 2021
Cited by 15 | Viewed by 2719
Abstract
The subject of the present paper is the investigation of a new type of solitons, called η-∗-Ricci solitons in (k,μ)-almost co-Kähler manifold (briefly, ackm), which generalizes the notion of the η-Ricci soliton [...] Read more.
The subject of the present paper is the investigation of a new type of solitons, called η-∗-Ricci solitons in (k,μ)-almost co-Kähler manifold (briefly, ackm), which generalizes the notion of the η-Ricci soliton introduced by Cho and Kimura. First, the expression of the ∗-Ricci tensor on ackm is obtained. Additionally, we classify the η-∗-Ricci solitons in (k,μ)-ackms. Next, we investigate (k,μ)-ackms admitting gradient η-∗-Ricci solitons. Finally, we construct two examples to illustrate our results. Full article
(This article belongs to the Special Issue Geometry of Manifolds and Applications)
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