Proposed theorems on an almost complex golden structure and its frame bundle
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Abstract
The goal of this research is to ascertain the connection between CRstructure and an almost complex golden structure and to identify some fundamental findings. A few theorems on CR-structure and an almost complex golden structure are proved, and integrability criteria are discussed.
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Sadiyal, A. (2024). Proposed theorems on an almost complex golden structure and its frame bundle. Journal of the Tensor Society, 18(01), 01-08. https://doi.org/10.56424/jts.v18i01.250
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References
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[14] R. Kumar, L Colney, M.N.I. Khan, Lifts of a semi-symmetric non-metric
connection (SSNMC) from statistical manifolds to the tangent Bundle Results in Nonlinear Analysis 6 (3), 50-65, 2023.
[15] R. Kumar, L Colney, M.N.I. Khan, Proposed Theorems on the Lifts of
Kenmotsu Manifolds Admitting a Non-Symmetric Non-Metric Connection
(NSNMC) in the Tangent Bundle, Symmetry 15(11), 2037, 2023.
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Bundles. Springer Netherlands, Kluwer Academic Publishers, 1989.
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Frame Bundle of an Almost Contact Metric Manifold. Math. Z. 1986, 193,
431-440.
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bundle. Annali di Matematica pura ed applicata. 1986, 143, 123–141.
https://doi.org/10.1007/BF01769212
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Inc., New York, 1973.
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Solitons Fractals 1997, 8(10), 1631–1643.
[22] Stakhov, A., The generalized golden proportions, a new theory of real
numbers, and ternary mirror-symmetrical arithmetic, Chaos, Solitons and
Fractals 2007, 33, 315–334.
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Rend Di Mat Di Roma 1983, 3, 577-592.
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Singapore: World Scientific, 1984.
[26] Goldberg, S.I.; Yano, K. Polynomial structures on manifolds, Kodai Math
Sem Rep. 1970, 22, 199-218.
[27] Goldberg, S.I.; Petridis, N.C. Differentiable solutions of algebraic equations on manifolds. Kodai Math. Sem. Rep. 1973, 25, 111–128.
[28] Ozkan, M.; Prolongations of golden structures to tangent bundles. Differential Geometry Dynamical Systems 2014, 16, 227-239.
[29] Ozkan, M.; Peltek, B. A New Structure on Manifolds: Silver Structure,
International Electronic Journal of Geometry, 2016, 9(2), 59–69.
[30] Gonul, S.; Erken, I. K.; Yazla, A.; Murathan, C. A Neutral relation
between metallic structure and almost quadratic ϕ-structure. Turk J Math.
2019, 43, 268-278.
[31] Lachieze-Rey M. Connections and Frame Bundle Reductions.
arXiv:2002.01410 [math-ph], 4 Feb 2020.
[2] A. Bejancu, CR submanifolds of a Kaehler manifold-I, Proc. Amer. Math. Soc. 69 (1978), 135-142.
[3] D.E. Blair and B.Y. Chen, On CR-submanifolds of Hermitian manifolds, Israel J. Math. 34 (1979), 353-363.
[4] B.Y. Chen, Geometry of submanifolds, Marcel Dekker, New York, (1973).
[5] S. Dragomir, M. H. Shahid and F.R. Al-Solamy, Geometry of CauchyRiemann Submanifolds, Springer Singapore, (2016).
[6] Lovejoy S. Das, Submanifolds of F-structure satisfying FK +(−)K+1F = 0, Internat. J. Math. Math. Sci. 26 (2001), 167-172.
[7] Lovejoy S. Das, On CR-structure and F-structure satisfying FK + (−)K+1F = 0. Rocky Mountain Journal of Mathematics, 36(3) (2006),
885-892.
[8] K. Yano and Masahiro Kon, Differential geometry of CR-submanifolds, Geom. Dedicata 10 (1981), 369-391.
[9] M.N.I. Khan, S Chaubey, N Fatima, A Al Eid, Metallic Structures for Tangent Bundles over Almost Quadratic –Manifolds, Mathematics 11, 4683,
2023.
[10] U.C. De, M.N.I. Khan, Complete lifts of a semi-symmetric non-metric connection from a riemannian manifold to its tangent bundles, Commun.
Korean Math. Soc. 38 (4), 1233-1247, 2023.
[11] M.N.I. Khan, F Mofarreh, A Haseeb, Tangent Bundles of P-Sasakian Manifolds Endowed with a Quarter-Symmetric Metric Connection, Symmetry, 2023 15 (3), 753.
[12] M.N.I. Khan, De, U.C.; Velimirovic, L.S. Lifts of a Quarter-Symmetric
Metric Connection from a Sasakian Manifold to Its Tangent Bundle. Mathematics, 11, 53, 2023.
[13] M.N.I. Khan, Novel theorems for metallic structures on the frame bundle
of the second order, Filomat 36:13 (2022), 4471–4482, 2022.
[14] R. Kumar, L Colney, M.N.I. Khan, Lifts of a semi-symmetric non-metric
connection (SSNMC) from statistical manifolds to the tangent Bundle Results in Nonlinear Analysis 6 (3), 50-65, 2023.
[15] R. Kumar, L Colney, M.N.I. Khan, Proposed Theorems on the Lifts of
Kenmotsu Manifolds Admitting a Non-Symmetric Non-Metric Connection
(NSNMC) in the Tangent Bundle, Symmetry 15(11), 2037, 2023.
8[16] Cordero, L.A.; Dodson, C.T.; Le´on, M.D. Differential Geometry of Frame
Bundles. Springer Netherlands, Kluwer Academic Publishers, 1989.
[17] Bonome, A.; Castro, R.; Hervella, L.M. Almost Complex Structure in the
Frame Bundle of an Almost Contact Metric Manifold. Math. Z. 1986, 193,
431-440.
[18] Cordero, L.A.; Leon, D.M. Prolongation of G-structures to the frame
bundle. Annali di Matematica pura ed applicata. 1986, 143, 123–141.
https://doi.org/10.1007/BF01769212
[19] Yano, K.; Ishihara, S. Tangent and Cotangent Bundles. Marcel Dekker,
Inc., New York, 1973.
[20] Crasmareanu, M.; Hretcanu, C.E. Golden differential geometry. Chaos
Solitons Fractals 2008, 38, 1229-1238.
[21] Spinadel, V.W. de., On characterization of the onset to chaos, Chaos
Solitons Fractals 1997, 8(10), 1631–1643.
[22] Stakhov, A., The generalized golden proportions, a new theory of real
numbers, and ternary mirror-symmetrical arithmetic, Chaos, Solitons and
Fractals 2007, 33, 315–334.
[23] Naveira A. A classification of Riemannian almost-product manifolds.
Rend Di Mat Di Roma 1983, 3, 577-592.
[24] Pitis G. On some submanifolds of a locally product manifold. Kodai Math
J. 1986, 9, 327-333.
[25] Yano K, Kon M. Structures on Manifolds, Series in Pure Mathematics.
Singapore: World Scientific, 1984.
[26] Goldberg, S.I.; Yano, K. Polynomial structures on manifolds, Kodai Math
Sem Rep. 1970, 22, 199-218.
[27] Goldberg, S.I.; Petridis, N.C. Differentiable solutions of algebraic equations on manifolds. Kodai Math. Sem. Rep. 1973, 25, 111–128.
[28] Ozkan, M.; Prolongations of golden structures to tangent bundles. Differential Geometry Dynamical Systems 2014, 16, 227-239.
[29] Ozkan, M.; Peltek, B. A New Structure on Manifolds: Silver Structure,
International Electronic Journal of Geometry, 2016, 9(2), 59–69.
[30] Gonul, S.; Erken, I. K.; Yazla, A.; Murathan, C. A Neutral relation
between metallic structure and almost quadratic ϕ-structure. Turk J Math.
2019, 43, 268-278.
[31] Lachieze-Rey M. Connections and Frame Bundle Reductions.
arXiv:2002.01410 [math-ph], 4 Feb 2020.