Geometry of Kenmotsu Manifolds via Q-Curvature Tensor and Schouten–Van Kampen Connection - Mustafa Yıldırım; Selahattin Beyendi; Gülhan Ayar; Nesip Aktan (Axioms, 2025)
This research paper aims to study the Q-curvature tensor on Kenmotsu manifolds endowed with the Schouten–van Kampen connection. Using the Q-curvature tensor, whose trace is the well-known Z-tensor, we characterized Kenmotsu manifolds by introducing the notion of <semantics>ζ</semantics>-<semantics><mover accent="true">Q˜</mover></semantics> flat and <semantics>ϕ</semantics>-<semantics><mover accent="true">Q˜</mover></semantics> flat manifolds and novel tensor conditions, such as <semantics><mover accent="true">Q˜</mover>(ξ,X)<mover accent="true">Q˜</mover>=0, </semantics><semantics><mover accent="true">Q˜</mover>(ξ,X)<mover accent="true">R˜</mover>=0, </semantics><semantics><mover accent="true">Q˜</mover>(ξ,X)<mover accent="true">C˜</mover>=0, </semantics><semantics><mover accent="true">Q˜</mover>(ξ,X)<mover accent="true">S˜</mover>=0</semantics>, <semantics><mover accent="true">Q˜</mover>(ξ,X)<mover accent="true">H˜</mover>=0</semantics>, and <semantics><mover accent="true">Q˜</mover>(ξ,X)<mover accent="true">P˜</mover>=0</semantics>, 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.