A note on curvature-like invariants of some connections on locally decomposable spaces | Zendy

Nevena Pusic | Zendy

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A note on curvature-like invariants of some connections on locally decomposable spaces

Author(s) -

Nevena Pusic

Publication year - 2013

Publication title -

publications de l institut mathematique

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.246

H-Index - 17

eISSN - 1820-7405

pISSN - 0350-1302

DOI - 10.2298/pim1308219p

Subject(s) - riemann curvature tensor , curvature , mathematics , tensor product , invariant (physics) , conformal map , pure mathematics , space (punctuation) , tensor (intrinsic definition) , tensor product of hilbert spaces , transformation (genetics) , product (mathematics) , mathematical analysis , tensor contraction , geometry , mathematical physics , computer science , biochemistry , chemistry , gene , operating system

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 AB, 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.

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