Geodesic
A Note on Curvature-like Invariants of Some Connections on Locally Decomposable Spaces
Publications de l'Institut Mathématique, _N_S_94 (2013) no. 108, p. 219 .

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We consider an $n$-dimensional locally product space with $p$ and $q$ dimensional components $(p+q=n)$ with parallel structure tensor, what 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, $(F,g)$-holomorphically semisymmetric one and $F$-holomorphically semisymmetric one, both with gradient generators. They both have curvature-like invariants and they are both equal to $PC$-tensor.
Classification : 53A30 53A40 53B15
Keywords: locally product space, conformal transformation, $PC-$ curvature tensor, class of holomorphically semisymmetric connections, Kähler-type identities 
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     author = {Nevena Pu\v{s}i\'c},
     title = {A {Note} on {Curvature-like} {Invariants} of {Some} {Connections} on {Locally} {Decomposable} {Spaces}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {219 },
     publisher = {mathdoc},
     volume = {_N_S_94},
     number = {108},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_2013_N_S_94_108_a21/}
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Nevena Pušić. A Note on Curvature-like Invariants of Some Connections on Locally Decomposable Spaces. Publications de l'Institut Mathématique, _N_S_94 (2013) no. 108, p. 219 . http://geodesic.mathdoc.fr/item/PIM_2013_N_S_94_108_a21/