EMIS ELibM Electronic Journals Publications de l'Institut Mathématique, Nouvelle Série
Vol. 94(108), pp. 219–228 (2013)

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A NOTE ON CURVATURE-LIKE INVARIANTS OF SOME CONNECTIONS ON LOCALLY DECOMPOSABLE SPACES

Nevena Pusic

Department of Mathematics and Computer Science, Faculty of Science, University of Novi Sad, Novi Sad, Serbia

Abstract: 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.

Keywords: locally product space, conformal transformation, $PC-$ curvature tensor, class of holomorphically semisymmetric connections, Kähler-type identities

Classification (MSC2000): 53A30; 53A40, 53B15

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Electronic fulltext finalized on: 8 Nov 2013. This page was last modified: 22 Nov 2013.

© 2013 Mathematical Institute of the Serbian Academy of Science and Arts
© 2013 FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition