The Geometry of Golden Conjugate Connections
DOI:
https://doi.org/10.5644/SJM.10.2.09Keywords:
Golden structure, (conjugate) linear connection, Golden Riemannian manifold, structural and virtual tensor fieldAbstract
Properties of Golden conjugate connections are stated by pointing out their relation to product conjugate connections. We define the analogues in Golden geometry of the structural and the virtual tensors from the almost product geometry and express the Golden conjugate connections in terms of these tensors.
2010 Mathematics Subject Classification. 53C07, 53C15, 53C25.
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References
A. Bejancu; H. R. Farran, Foliations and geometric structures, Mathematics and Its Applications 580, Springer, Dordrecht, 2006. MR2190039 (2006j:53034)
A. M. Blaga and M. Crasmareanu, The geometry of complex conjugate connections, Hacet. J. Math. Stat., 41 (1) (2012), 119-126, MR2976917.
A. M. Blaga and M. Crasmareanu, The geometry of product conjugate connections, An. Stiint. Univ. Al. I. Cuza Ia¸si Mat. (N. S.), 59 (1) (2013), 73-84, MR3098381.
F. Bullo and A. D. Lewis, Geometric control of mechanical systems. Modeling, analysis, and design for simple mechanical control systems, Texts in Applied Mathematics, 49, Springer-Verlag, New York, 2005. MR2099139 (2005h:70030).
M. Crasmareanu and C.-E. Hret¸canu, Golden Differential Geometry, Chaos Solitons Fractals, 38 (5) (2008), 1229-1238, MR2456523 (2009k:53059).
A. Gezer, N. Cengiz and A. Salimov, On integrability of Golden Riemannian structures, Turkish J. Math., 37 (2013), 693-703, MR3070945.
C.-E. Hret¸canu and M. Crasmareanu, On some invariant submanifolds in Riemannian manifold with Golden Structure, An. S¸tiint¸. Univ. Al. I. Cuza Ia¸si Mat., 53 (2007), Supl., 199-211. MR2522394 (2011e:53012).
C.-E. Hret¸canu and M. Crasmareanu, Applications of the golden ratio on Riemannian manifolds, Turkish J. Math., 33 (2) (2009), 179-191, MR2537561 (2010d:53035).
F. Ozdemir and M. Crasmareanu, ¨ Geometrical objects associated to a substructure, Turkish J. Math., 35 (4) (2011), 717-728, MR2896417.