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Manifolds endowed with torsion and nonmetricity are interesting both from the physical and the mathematical points of view.
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N. J. Hitchin, “Complex manifolds and Einstein equations, twistor geometry and nonlinear systems” (eds H. D. Doebner and T. D. Palev), Lecture Notes in Math. 970
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É. Cartan, “Sur les variétés à connexion affine et la théorie de la relativité généralisée,” (Gauthier Villars, 1955). See also “On manifolds with an affine connection and the theory of general relativity”, transl. A. Magnon and A. Ashtekar (Bibliopolis, Napoli, 1986)
1986
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L. L. Smalley, “Brans-Dicke type models with nonmetricity,” Phys. Rev. D 33
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J. W. Maluf, “Conformal invariance and torsion in general relativity,” Gen. Rel. Grav. 19
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1990
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R. S. Ward, “Einstein-Weyl spaces and SU( ∞ \infty ) Toda fields,” Class. Quant. Grav. 7
1990
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P. D. Mannheim, “Conformal cosmology with no cosmological constant,” Gen. Rel. Grav. 22
1990
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J. Stelmach, “Nonmetricity driven inflation,” Class. Quant. Grav. 8
1991
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H. Pedersen and K. P. Tod, “Einstein metrics and hyperbolic monopoles,” Class. Quantum Grav. 8
1991
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K. P. Tod, “Compact 3-dimensional Einstein-Weyl structures,” J. London Math. Soc. s2-45
1992
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H. Pedersen and K. P. Tod, “Three-dimensional Einstein-Weyl geometry,” Adv. Math. 97
1993
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P. Baekler, N. Boulanger and F. W. Hehl, “Linear connections with propagating spin-3 field in gravity,” Phys. Rev. D 74
2006
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2009
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H. Pedersen and A. Swann, “Riemannian submersions, four-manifolds and Einstein-Weyl geometry,” Proc. London Math. Soc. s3-66
1993
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H. Pedersen and A. F. Swann, “Einstein-Weyl geometry, the Bach tensor and conformal scalar curvature,” J. reine angew. Math. 441
1993
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H. Pedersen, Y. S. Poon and A. F. Swann, “The Einstein-Weyl equations in complex and quaternionic geometry”, Differential Geometry and its Applications 3
1993
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E. A. Poberii, “Nonmetricity driven inflation,” Helv. Phys. Acta 67
1994
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H. Pedersen, Y. S. Poon and A. F. Swann, “The Hitchin-Thorpe inequality for Einstein-Weyl manifolds”, Bull. London Math. Soc. 26
1994
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W. Drechsler and D. Hartley, “The role of the internal metric in generalized Kaluza-Klein theories,” J. Math. Phys. 35
1994
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2009
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2010
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2010
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2010
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A. C. Ferreira, “Einstein four-manifolds with skew torsion,” J. Geom. Phys. 61
2011
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2012
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2012
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2012
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2012
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L. Fabbri, “Metric-torsional conformal gravity,” Phys. Lett. B 707
2012
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M. Blagojevic and F. Hehl (eds.), “Gauge Theories of Gravitation,” Imperial College Press, London 2013
2013
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2014
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2014
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C. Pagani and R. Percacci, “Quantum gravity with torsion and nonmetricity,” Class. Quant. Grav. 32
2015
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2016
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2016
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P. Luz and V. Vitagliano, “Raychaudhuri equation in spacetimes with torsion,” Phys. Rev. D 96
2017
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J. Beltrán Jiménez and T. S. Koivisto, “Modified gravity with vector distortion and cosmological applications,” Universe 3
2017
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2017
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2017
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2017
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2018
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J. T. Wheeler, “Weyl geometry,” Gen. Rel. Grav. 50
2018
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2018
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I. P. Lobo and C. Romero, “Experimental constraints on the second clock effect,” Phys. Lett. B 783
2018
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S. Chakrabarty and A. Lahiri, “Different types of torsion and their effect on the dynamics of fields,” Eur. Phys. J. Plus 133
2018
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2019
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