A NEW CLASS OF $F$-STRUCTURES: INTEGRABILITY AND EXAMPLES

In the paper, we present a new class of $F$-structures characterised by the equation $a F^{2K+1} +b F^{2K} +c F^{K} +(-1)^{K} F=0$, where $K$ is a positive integer with $K\geq3$ and $a$, $b$, and $c$ are real or complex numbers. We study the problems of integrability, partial integrability and complete integrability for these structures. In addition, we provide illustrative examples that demonstrate the application of these structures.