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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.
53A30 Conformal differential geometry (MSC2010)
53A40 Other special differential geometries
53A55 Differential invariants (local theory), geometric objects
53B15 Other connections
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