On the Geometry of Kobayashi–Nomizu Type and Yano Type Connections on the Tangent Bundle with Sasaki Metric
In this paper, we address the study of the Kobayashi–Nomizu type and the Yano type connections on the tangent bundle <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>T</mi><mi>M</mi...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-09-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/11/18/3865 |
| _version_ | 1797578959988195328 |
|---|---|
| author | Esmaeil Peyghan Davood Seifipour Ion Mihai |
| author_facet | Esmaeil Peyghan Davood Seifipour Ion Mihai |
| author_sort | Esmaeil Peyghan |
| collection | DOAJ |
| description | In this paper, we address the study of the Kobayashi–Nomizu type and the Yano type connections on the tangent bundle <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>T</mi><mi>M</mi></mrow></semantics></math></inline-formula> 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. |
| first_indexed | 2024-03-10T22:30:04Z |
| format | Article |
| id | doaj.art-79f01f77946749b3a20af5e2a1af4bc4 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T22:30:04Z |
| publishDate | 2023-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-79f01f77946749b3a20af5e2a1af4bc42023-11-19T11:48:41ZengMDPI AGMathematics2227-73902023-09-011118386510.3390/math11183865On the Geometry of Kobayashi–Nomizu Type and Yano Type Connections on the Tangent Bundle with Sasaki MetricEsmaeil Peyghan0Davood Seifipour1Ion Mihai2Department of Mathematics, Faculty of Science, Arak University, Arak 38156-88349, IranDepartment of Mathematics, Abadan Branch, Islamic Azad University, Abadan 63176-36531, IranDepartment of Mathematics, University of Bucharest, 010014 Bucharest, RomaniaIn this paper, we address the study of the Kobayashi–Nomizu type and the Yano type connections on the tangent bundle <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>T</mi><mi>M</mi></mrow></semantics></math></inline-formula> 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.https://www.mdpi.com/2227-7390/11/18/3865Codazzi manifoldKobayashi–Nomizu type connectionmutual curvatureYano type connection |
| spellingShingle | Esmaeil Peyghan Davood Seifipour Ion Mihai On the Geometry of Kobayashi–Nomizu Type and Yano Type Connections on the Tangent Bundle with Sasaki Metric Mathematics Codazzi manifold Kobayashi–Nomizu type connection mutual curvature Yano type connection |
| title | On the Geometry of Kobayashi–Nomizu Type and Yano Type Connections on the Tangent Bundle with Sasaki Metric |
| title_full | On the Geometry of Kobayashi–Nomizu Type and Yano Type Connections on the Tangent Bundle with Sasaki Metric |
| title_fullStr | On the Geometry of Kobayashi–Nomizu Type and Yano Type Connections on the Tangent Bundle with Sasaki Metric |
| title_full_unstemmed | On the Geometry of Kobayashi–Nomizu Type and Yano Type Connections on the Tangent Bundle with Sasaki Metric |
| title_short | On the Geometry of Kobayashi–Nomizu Type and Yano Type Connections on the Tangent Bundle with Sasaki Metric |
| title_sort | on the geometry of kobayashi nomizu type and yano type connections on the tangent bundle with sasaki metric |
| topic | Codazzi manifold Kobayashi–Nomizu type connection mutual curvature Yano type connection |
| url | https://www.mdpi.com/2227-7390/11/18/3865 |
| work_keys_str_mv | AT esmaeilpeyghan onthegeometryofkobayashinomizutypeandyanotypeconnectionsonthetangentbundlewithsasakimetric AT davoodseifipour onthegeometryofkobayashinomizutypeandyanotypeconnectionsonthetangentbundlewithsasakimetric AT ionmihai onthegeometryofkobayashinomizutypeandyanotypeconnectionsonthetangentbundlewithsasakimetric |