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Dergiler / International Electronic Journal of Geometry / 2019 / Cilt: 12 - Sayı: 2

Schouten and Vr˘anceanu Connections on Golden Manifolds

Erol KILIÇ
Sadık KELEŞ
Mustafa GÖK
Sayfa
169–181
Yayın Tarihi
2022-10-18
DOI
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Finally,we analyze the notion of geodesicity on golden manifolds in terms of the Schouten and Vr˘anceanuconnections.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this paper, we study two special linear connections, which are called Schouten and Vr˘anceanuconnections, defined by an arbitrary fixed linear connection on a differentiable manifoldadmitting a golden structure.
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Temel Bulgular & Veri:The golden structure defines two naturally complementary projectionoperators splitting the tangent bundle into two complementary parts, so there are two globallycomplementary distributions of the tangent bundle.
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Sonuç & Katkı:Finally,we analyze the notion of geodesicity on golden manifolds in terms of the Schouten and Vr˘anceanuconnections.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

Abstract

In this paper, we study two special linear connections, which are called Schouten and Vr˘anceanuconnections, defined by an arbitrary fixed linear connection on a differentiable manifoldadmitting a golden structure. The golden structure defines two naturally complementary projectionoperators splitting the tangent bundle into two complementary parts, so there are two globallycomplementary distributions of the tangent bundle. We examine the conditions of parallelismfor both of the distributions with respect to the fixed linear connection under the assumptionthat it is either the Levi-Civita connection or is not. We investigate the concepts of halfparallelism and anti half parallelism for each of the distributions with respect to the Schoutenand Vr˘anceanu connections. We research integrability conditions of the golden structure and itsassociated distributions from the viewpoint of the Schouten and Vr˘anceanu connections. Finally,we analyze the notion of geodesicity on golden manifolds in terms of the Schouten and Vr˘anceanuconnections.

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Bu Makaleye Atıf Yap

KILIÇ, E., KELEŞ, S., GÖK, M. (2022). Schouten and Vr˘anceanu Connections on Golden Manifolds. International Electronic Journal of Geometry, Cilt: 12 - Sayı: 2, 169–181. https://ajindex.com/articles/539625

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Kaynakça (9)

  1. Goldberg, S. I. and Yano, K., Polynomial Structures on Manifolds. Kodai Math. Sem. Rep. 22 (1970), no. 2, 199-218
  2. Hre¸tcanu, C. E., Submanifolds in Riemannian Manifolds with Golden Structure. Acta Math. Acad. Paedagog. Nyházi. (N.S.) 24 (2008), no. 1, 3-4
  3. Crâ¸sm˘areanu, M. C. and Hre¸tcanu, C. E., Golden Differential Geometry. Chaos Soliton. Fract. 38 (2008), no. 5, 1229-1238
  4. Hre¸tcanu, C.E. and Crâ¸sm˘areanu, M. C., On Some Invariant Submanifolds in a Riemannian Manifold with Golden Structure. An. ¸ Stiin¸t. Univ. Al. I. Cuza Ia¸si. Mat. (N.S.) 53 (2007), suppl. 1, 199-211
  5. Hre¸tcanu, C. E. and Crâ¸sm˘areanu, M. C., Applications of the Golden Ratio on Riemannian Manifolds. Turk. J. Math. 33 (2009), no. 2, 179-191
  6. Ianu¸s, S., Some Almost Product Structures on Manifolds with Linear Connection. Kodai Math. Sem. Rep. 23 (1971), no. 3, 305-310
  7. Das, L. S., Niki´c, J. and Nivas, R., Parallelism of Distributions and Geodesics on F (a1; a2;:::; an)-structure Lagrangian Manifolds. Differ. Geom. Dyn. Syst. 8 (2006), no. 1, 82-89
  8. Bejancu, A. and Farran, H. D., Foliations and Geometric Structures. Springer, Amsterdam, 2006
  9. Ianu¸s, S., Sur les Structures Presque Produit des Varietes a Connection Lineairei. C. R. Acad. Sci. 272 (1971), no. 11, 734-735.