Geometry of Kenmotsu Manifolds via <i>Q</i>-Curvature Tensor and Schouten–Van Kampen Connection

Geometry of Kenmotsu Manifolds via <i>Q</i>-Curvature Tensor and Schouten–Van Kampen Connection

This research paper aims to study the <i>Q</i>-curvature tensor on Kenmotsu manifolds endowed with the Schouten–van Kampen connection. Using the <i>Q</i>-curvature tensor, whose trace is the well-known Z-tensor, we characterized Kenmotsu manifolds by introducing the notion of...

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Bibliographic Details
Main Authors: Mustafa Yıldırım, Selahattin Beyendi, Gülhan Ayar, Nesip Aktan
Format: Article
Language:English
Published: MDPI AG 2025-06-01
Series:Axioms
Subjects:
Kenmotsu manifolds
Schouten van–Kampen connection
Q-curvature tensor
Online Access:https://www.mdpi.com/2075-1680/14/7/498
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Summary:This research paper aims to study the <i>Q</i>-curvature tensor on Kenmotsu manifolds endowed with the Schouten–van Kampen connection. Using the <i>Q</i>-curvature tensor, whose trace is the well-known Z-tensor, we characterized Kenmotsu manifolds by introducing the notion of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ζ</mi></semantics></math></inline-formula>-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover accent="true"><mi>Q</mi><mo>˜</mo></mover></semantics></math></inline-formula> flat and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ϕ</mi></semantics></math></inline-formula>-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover accent="true"><mi>Q</mi><mo>˜</mo></mover></semantics></math></inline-formula> flat manifolds and novel tensor conditions, such as <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mover accent="true"><mi>Q</mi><mo>˜</mo></mover><mrow><mo>(</mo><mi>ξ</mi><mo>,</mo><mi>X</mi><mo>)</mo></mrow><mover accent="true"><mi>Q</mi><mo>˜</mo></mover><mo>=</mo><mn>0</mn><mo>,</mo><mo> </mo></mrow></semantics></math></inline-formula><inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mover accent="true"><mi>Q</mi><mo>˜</mo></mover><mrow><mo>(</mo><mi>ξ</mi><mo>,</mo><mi>X</mi><mo>)</mo></mrow><mover accent="true"><mi>R</mi><mo>˜</mo></mover><mo>=</mo><mn>0</mn><mo>,</mo><mo> </mo></mrow></semantics></math></inline-formula><inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mover accent="true"><mi>Q</mi><mo>˜</mo></mover><mrow><mo>(</mo><mi>ξ</mi><mo>,</mo><mi>X</mi><mo>)</mo></mrow><mover accent="true"><mi>C</mi><mo>˜</mo></mover><mo>=</mo><mn>0</mn><mo>,</mo><mo> </mo></mrow></semantics></math></inline-formula><inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mover accent="true"><mi>Q</mi><mo>˜</mo></mover><mrow><mo>(</mo><mi>ξ</mi><mo>,</mo><mi>X</mi><mo>)</mo></mrow><mover accent="true"><mi>S</mi><mo>˜</mo></mover><mo>=</mo><mn>0</mn></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mover accent="true"><mi>Q</mi><mo>˜</mo></mover><mrow><mo>(</mo><mi>ξ</mi><mo>,</mo><mi>X</mi><mo>)</mo></mrow><mover accent="true"><mi>H</mi><mo>˜</mo></mover><mo>=</mo><mn>0</mn></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mover accent="true"><mi>Q</mi><mo>˜</mo></mover><mrow><mo>(</mo><mi>ξ</mi><mo>,</mo><mi>X</mi><mo>)</mo></mrow><mover accent="true"><mi>P</mi><mo>˜</mo></mover><mo>=</mo><mn>0</mn></mrow></semantics></math></inline-formula>, with the Schouten–van Kampen connection. To validate some of our results, we constructed a non-trivial example of Kenmotsu manifolds endowed with the Schouten–van Kampen connection.
ISSN:2075-1680

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