Abstract
In this paper we study the dual geometry of a normalized affinely connected space A n,n . In particular, we consider the dual affine-metrically connected spaces \( \mathop M\limits^p _{n,n} \) induced by a nondegenerate normalization of an affine-metrically connected space M n,n .
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References
G. F. Laptev, “Separation of One Class of Intrinsic Geometries Induced on a Surface in an Affinely Connected Domain,” Sov. Phys. Dokl. 41(8), 329–331 (1943).
A. V. Stolyarov, “Dual Geometry of a Normalized Affinely Connected Space,” Vestn. Chuvashsk. Gos. Ped. Univ., No. 4, 21–27 (2005).
A. P. Norden, Affinely Connectted Spaces (Nauka, Moscow, 1976) [in Russian].
A. V. Stolyarov, Dual Theory of Framed Manifolds (Chuvashsk. Gos. Ped. Inst., Cheboksary, 1994) [in Russian].
P. K. Rashevskii, Riemann Geometry and Tensor Analysis (Nauka, Moscow, 1967) [in Russian].
G. F. Laptev, “Differential Geometry of Immersed Manifolds,” Mosk.Matem. Ob-vo, No. 2, 275–382 (1953).
A. V. Stolyarov, “Space with Metric Projective Connection,” Izv. Vyssh. Uchebn. Zaved. Mat., No. 11, 70–76 (2003) [Russian Mathematics (Iz. VUZ) 47 (11), 66–72 (2003)].
A. V. Stolyarov, “Affine-Metric Connection,” Vestn. Chuvashsk. Gos. Ped. Univ., No. 5, 158–167 (2006).
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Original Russian Text © T.G. Alyonina, 2009, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2009, No. 7, pp. 65–70.
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Alyonina, T.G. Dual affine-metrically connected spaces. Russ Math. 53, 55–59 (2009). https://doi.org/10.3103/S1066369X09070068
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DOI: https://doi.org/10.3103/S1066369X09070068