The paper defines generalized almost plastic structures on TM⊕T*M, constructs a family from two compatible tensor fields, and gives integrability conditions.
Kurose, Statistical Manifolds Admitting Torsion, Geometry an d Something; Fukuoka Univ.: Fukuoka-shi (In Japanese) (2007)
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On generalized plastic structures
The paper defines generalized almost plastic structures on TM⊕T*M, constructs a family from two compatible tensor fields, and gives integrability conditions.