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On the geometry of complex ( κ , μ ) ‐spaces
Author(s) -
Yıldırım Handan
Publication year - 2016
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201500329
Subject(s) - homothetic transformation , mathematics , flatness (cosmology) , complex space , manifold (fluid mechanics) , conformal map , invariant (physics) , geometry , pure mathematics , curvature , space (punctuation) , mathematical analysis , affine transformation , mathematical physics , computer science , mechanical engineering , physics , cosmology , quantum mechanics , engineering , operating system
It is known that applying an H ‐homothetic deformation to a complex contact manifold whose vertical space is annihilated by the curvature yields a condition which is invariant under H ‐homothetic deformations. A complex contact manifold satisfying this condition is said to be a complex ( κ , μ ) ‐space. In this paper, we deal with the questions of Bochner, conformal and conharmonic flatness of complex ( κ , μ ) ‐spaces when κ < 1 , and prove that such kind of spaces cannot be Bochner flat, conformally flat or conharmonically flat.