참고문헌
- B. E. Acet, Lightlike hypersurfaces of metallic semi-Rieamnnian Manifolds, Int. J. Geom. Meth. M. (in press).
- P. Baird and J. C. Wood, Harmonic Morphisms Between Riemannian Manifolds, London Mathematical Society Monographs, No. 29, Oxford University Press, The Clarendon Press, Oxford, 2003.
- C.-L. Bejan and M. Crasmareanu, Parallel second order tensors and Ricci solitons in 3-dimensional normal paracontact geometry, Ann. Global Anal. Geom. 46(2) (2014), 117-127. https://doi.org/10.1007/s10455-014-9414-4
- D. E. Blair, Riemannian Geometry of Contact and Symplectic Manifolds, Birkhauser, Boston, (2002).
- C-E. Hretcanu and M. Crasmareanu, Metallic structures on Riemannian manifolds, Revista de la union matematica argentina 54(2) (2013), 15-27.
- M. Crasmareanu and C-E. Hretcanu, Golden differential geometry, Chaos, Solitons & Fractals, 38(5) (2008), 1229-1238. https://doi.org/10.1016/j.chaos.2008.04.007
- C-E. Hretcanu and M. C. Crasmareanu, Applications of the Golden Ratio on Riemannian Manifolds, Turk J. Math. 33(2) (2009), 179-191.
- M. Crasmareanu and L. I. Piscoran, Invariant distributions and holomorphic vector fields in paracontact geometry, Turkish J. Math. 39(4) (2015), 467-476. https://doi.org/10.3906/mat-1412-24
- H. Cayir, Some Notes on Lifts of Almost Paracontact Structures, American Review of Mathematics and Statistics. 3(1) (2015), 52-60.
- J. Eells and H. J. Sampson, Harmonic mappings of Riemannian Manifolds, Amer. J. Math. 86 (1964), 109-160. https://doi.org/10.2307/2373037
- S. Erdem, On product and Golden structures and harmonicty, Turk J Math 42 (2018), 444-470. https://doi.org/10.3906/mat-1606-112
- F. E. Erdogan, Transversal Lightlike Submanifolds of Metallic Semi-Riemannian Manifolds, Turk J. Math. 42 (2018), 3133-3148. https://doi.org/10.3906/mat-1804-88
- B. Fuglede, Harmonic morphisms between Riemannian Manifolds, Ann. Inst. Fourier(Grenoble). 28 (1978), 107-144. https://doi.org/10.5802/aif.691
- T. Ishihara, A mapping of Riemannian manifolds which preserves harmonic functions, J. Math. Kyoto Univ. 19 (1979), 215-229. https://doi.org/10.1215/kjm/1250522428
- S. Kaneyuki and F. L. Willams, Almost paracontact and parahodge structures on manifolds, Nagoya Math. J. 99 (1985), 173-187. https://doi.org/10.1017/S0027763000021565
- A. Gezer, N. Cengiz, A. Salimov, On integrability of Golden Riemannian structures, Turk J. Math. 37 (2013), 693-703.
- A. Gezer and C. Karaman, On metallic Riemannian structures, Turk J. Math. 39 (2015), 954-962. https://doi.org/10.3906/mat-1504-50
- N. O. Poyraz and E. Yasar, Lightlike hypersurfaces of a golden semi-Riemannian manifold, Mediterr J Math 14 (2017), 204. https://doi.org/10.1007/s00009-017-0999-2
- M. Ozkan, Prolongations of golden structures to tangent bundles, Differ Geom Dyn Syst 16 2014, 227-238.
- M. Ozkan, A. C itlak, E. Taylan, Prolongations of Golden Structure to Tangent Bundle of Order 2, Gazi University Journal of Science, 28(2) (2015), 253-258.
- M. Ozkan, F. Yilmaz, Metallic structures on differentiable manifolds, Journal of Science and arts, 3 (2018), 645-660.
- A. Salimov, H. Cayir, Some Notes On Almost Paracontact Structures, Comptes Rendus de l'Academie Bulgare des Sciences. 66(3) (2013), 331-338.
- V. W. de Spinadel, On characterization of the onset to chaos, Chaos, Solitions & Fractals, 8(10) (1997), 1631-1643. https://doi.org/10.1016/S0960-0779(97)00001-5
- V. W. de Spinadel, The metallic means family and multifractal spectra, Nonlinear Anal. Ser. B: Real World Appl. 36(6) (1999), 721-745. https://doi.org/10.1016/S0362-546X(98)00123-0
- V. W. de Spinadel, The family of metallic means, Vis. Math. 1(3) (1999), http.//vismath1.tripod.com/spinadel/.
- V. W. de Spinadel, The metallic means family and forbidden symmetries, Int. Math. J. 2(3) (2002) 279-288.
- V. W. de Spinadel, The metallic means family and renormalization group techniques, Proc. Steklov Inst. Math., Control in Dynamic systems, suppl. 1 (2000), 194-209.
- B. Sahin, Almost poly-Norden Manifolds, International Journal of Maps in Mathematics, 1(1), (2018), 68-79.
- B. Sahin and M. A. Akyol, Golden maps between Golden Riemannian manifolds and constancy of certain maps, Math. Commun. 19 (2014), 333-342.
- K. Yano and M. Kon, Structures on Manifolds, World Scientific, Singapuore, Series in pure mathematics, 3 (1984).
- S. Zamkovoy, Canonical connections on paracontact manifolds, Ann. Glob. Anal. Geom. 36 (2009), 37-60. https://doi.org/10.1007/s10455-008-9147-3