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A note on curvature-like invariants of some connections on locally decomposable spaces. (English) Zbl 1299.53018
Summary: We consider an $$n$$-dimensional locally product space with $$p$$- and $$q$$-dimensional components $$(p+q=n)$$ with parallel structure tensor, which means that such a space is locally decomposable. If we introduce a conformal transformation on such a space, it will have an invariant curvature-type tensor, the so-called product conformal curvature tensor (PC-tensor). Here we consider two connections, the $$(F,g)$$-holomorphically semisymmetric one and the $$F$$-holomorphically semisymmetric one, both with gradient generators. They both have curvature-like invariants and they are both equal to PC-tensor.
##### MSC:
 53A30 Conformal differential geometry (MSC2010) 53A40 Other special differential geometries 53A55 Differential invariants (local theory), geometric objects 53B15 Other connections
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