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Adapted connections on foliated manifolds | ||
| Journal of Finsler Geometry and its Applications | ||
| دوره 7، شماره 1، 2026، صفحه 94-102 اصل مقاله (296.75 K) | ||
| نوع مقاله: Original Article | ||
| شناسه دیجیتال (DOI): 10.22098/jfga.2025.17686.1165 | ||
| نویسندگان | ||
| Zohreh Nazari* ؛ Elham Zangiabadi | ||
| Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran | ||
| چکیده | ||
| In this study, we define the local components of the adapted connection relative to the adapted frame field. We also calculate the covariant derivative of a tensor with respect to this connection. Furthermore, we present a classification of totally geodesic foliations and bundle-like metrics, along with the introduction of the local components of the torsion tensor associated with this connection. To illustrate our findings, we provide a relevant example. | ||
| کلیدواژهها | ||
| foliation؛ adapted connection؛ distribution | ||
| مراجع | ||
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1. A. Bejancu, Schouten-Van Kampen and Vra˘nceanu connnections on foliated manifolds, Anale. Stin. Univ. AL.I. CUZU. IASI, Tomul LII, Math. (2006), 37-60. 2. A. Bejancu and H R and Farran, Foliation and Geometric structures, Mathematics and Its Applications, springer, Dordrecht, 2006. 3. A. Fridmann and J. A. Schouten, U¨ber die Geometrie der halbsymmeMatrischen U¨bertragungen, Math. Z. 21 (1924), 211-223. 4. B. O;Neill, Semi-Riemannian geometry with applications to relativity, Academic Press,London, 1983. 5. B. L. Reinhart, Foliated manifolds with bundle-like metric, Ann. Math. 69(1959), 119-132. 6. J. A. Schouten, Ricci-Calculus, An introduction to tensor analysis and geometrical applications, Springer-Verlag, Berlin-G¨ ottingen-Heidelberg, 1954. 7. J. A. Schouten and E.R. Van Kampen, Zur Einbettungs-und Kru¨mmungstheorie nichtholonomer Gebilde, Math. Ann. 103(1930), 752-783. 8. G. Vr˘ anceanu, Sur quelques points de Ia theorie des espaces non holonomes, Bul. Fac.St. Cern˘ auti. 5(1931), 177-205. 9. I. Vaisman, Varie´te´s riemanniennes feuillete´es, Czech. Math. J. 21(1971), 46-75. | ||
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