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Infinitesimal Paraholomorphically Projective Transformation On Cotangent Bundle With Riemannian Extension

Yıl 2020, Cilt: 10 Sayı: 4, 2872 - 2880, 15.12.2020
https://doi.org/10.21597/jist.703428

Öz

The main purpose of the present paper is to study some properties of infinitesimal paraholomorphically projective transformation on 𝑇∗𝑀 with respect to the Levi-Civita connection of the Riemannian extension ( 𝑅∇) and adapted almost paracomplex structure 𝐽. Moreover, if 𝑇∗𝑀 be admits a non-affine infinitesimal paraholomorphically projective transformation, than 𝑀 and 𝑇∗𝑀 are locally flat.

Kaynakça

  • Aslanci S, Kazimova S and Salimov A A, 2010. Some remarks concerning Riemannian extensions. Ukrainian Mathematical Journal, 62(5): 661-675.
  • Bilen L, 2019. Projective Vector Fields on the Cotangent Bundle with Modified Riemannian Extension. Journal of the Institute of Science and Technology, 9(1): 389-396.
  • Cruceanu V, Gadea PM and Munoz Masque J, 1995. Para-Hermitian and Para-Kahler Manifolds. Quaderni Inst. Math. Messina, 2: 1-70.
  • Etayo F and Gadea PM, 1992. Paraholomorphically projective vector field. An. St.Univ."Al. I. Cuza" Iaşi Sect. a Mat. (N. S.), 38: 201-210.
  • Gezer A, 2011. On infinitesimal holomorfically projective transformations on the tangent bundles with respect to the Sasaki metric. Proc. Est. Acad. Sci, 60(3): 149-157
  • Hasegawa I and Yamauchi K, 1979. On infinitesimal holomorphically projective transformations in compact Kaehlerian manifolds. Hokkaido Math. J, 8: 214–219.
  • Hasegawa I and Yamauchi K, 2003. Infinitesimal holomorphically projective transformations on the tangent bundles with horizontal lift connection and adapted almost complex structure. J. Hokkaido Univ. Education, 53: 1–8.
  • Hasegawa I and Yamauchi K, 2005. Infinitesimal holomorphically projective transformations on the tangent bundles with complete lift connection. Differ. Geom. Dyn. Syst, 7: 42–48.
  • Iscan M and Magden A, 2008. Infinitesimal paraholomorphically projective transformations on tangent bundles with diagonal lift connection. Differential Geometry - Dynamical Systems, Vol.10: 170-177.
  • Patterson E M and Walker A G, 1952. Riemannian extensions. Quant. J. Math, 3: 19–28.
  • Prvanovic M, 1971. Holomorphically projective transformations in a locally product spaces. Math. Balkanika (N.S.), 1: 195-213.
  • Salimov A A, Iscan M and Etayo F, 2007. Paraholomorphic B-manifold and its properties. Topology and its Application, 154: 925-933.
  • Tarakci O, Gezer A and Salimov A A, 2009. On solutions of IHPT equations on tangent bundle with the metric II+III. Math.Comput. Modelling, 50: 953–958.
  • Yano K, Ishihara S, 1973. Tangent and cotangent bundles. Marcel Dekker, Inc. New York.

Infinitesimal Paraholomorphically Projective Transformation On Cotangent Bundle With Riemannian Extension

Yıl 2020, Cilt: 10 Sayı: 4, 2872 - 2880, 15.12.2020
https://doi.org/10.21597/jist.703428

Öz

The main purpose of the present paper is to study some properties of infinitesimal paraholomorphically projective transformation on 𝑇∗𝑀 with respect to the Levi-Civita connection of the Riemannian extension ( 𝑅∇) and adapted almost paracomplex structure 𝐽. Moreover, if 𝑇∗𝑀 be admits a non-affine infinitesimal paraholomorphically projective transformation, than 𝑀 and 𝑇∗𝑀 are locally flat.

Kaynakça

  • Aslanci S, Kazimova S and Salimov A A, 2010. Some remarks concerning Riemannian extensions. Ukrainian Mathematical Journal, 62(5): 661-675.
  • Bilen L, 2019. Projective Vector Fields on the Cotangent Bundle with Modified Riemannian Extension. Journal of the Institute of Science and Technology, 9(1): 389-396.
  • Cruceanu V, Gadea PM and Munoz Masque J, 1995. Para-Hermitian and Para-Kahler Manifolds. Quaderni Inst. Math. Messina, 2: 1-70.
  • Etayo F and Gadea PM, 1992. Paraholomorphically projective vector field. An. St.Univ."Al. I. Cuza" Iaşi Sect. a Mat. (N. S.), 38: 201-210.
  • Gezer A, 2011. On infinitesimal holomorfically projective transformations on the tangent bundles with respect to the Sasaki metric. Proc. Est. Acad. Sci, 60(3): 149-157
  • Hasegawa I and Yamauchi K, 1979. On infinitesimal holomorphically projective transformations in compact Kaehlerian manifolds. Hokkaido Math. J, 8: 214–219.
  • Hasegawa I and Yamauchi K, 2003. Infinitesimal holomorphically projective transformations on the tangent bundles with horizontal lift connection and adapted almost complex structure. J. Hokkaido Univ. Education, 53: 1–8.
  • Hasegawa I and Yamauchi K, 2005. Infinitesimal holomorphically projective transformations on the tangent bundles with complete lift connection. Differ. Geom. Dyn. Syst, 7: 42–48.
  • Iscan M and Magden A, 2008. Infinitesimal paraholomorphically projective transformations on tangent bundles with diagonal lift connection. Differential Geometry - Dynamical Systems, Vol.10: 170-177.
  • Patterson E M and Walker A G, 1952. Riemannian extensions. Quant. J. Math, 3: 19–28.
  • Prvanovic M, 1971. Holomorphically projective transformations in a locally product spaces. Math. Balkanika (N.S.), 1: 195-213.
  • Salimov A A, Iscan M and Etayo F, 2007. Paraholomorphic B-manifold and its properties. Topology and its Application, 154: 925-933.
  • Tarakci O, Gezer A and Salimov A A, 2009. On solutions of IHPT equations on tangent bundle with the metric II+III. Math.Comput. Modelling, 50: 953–958.
  • Yano K, Ishihara S, 1973. Tangent and cotangent bundles. Marcel Dekker, Inc. New York.
Toplam 14 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Matematik / Mathematics
Yazarlar

Lokman Bilen 0000-0001-8240-5359

Yayımlanma Tarihi 15 Aralık 2020
Gönderilme Tarihi 13 Mart 2020
Kabul Tarihi 7 Haziran 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 10 Sayı: 4

Kaynak Göster

APA Bilen, L. (2020). Infinitesimal Paraholomorphically Projective Transformation On Cotangent Bundle With Riemannian Extension. Journal of the Institute of Science and Technology, 10(4), 2872-2880. https://doi.org/10.21597/jist.703428
AMA Bilen L. Infinitesimal Paraholomorphically Projective Transformation On Cotangent Bundle With Riemannian Extension. Iğdır Üniv. Fen Bil Enst. Der. Aralık 2020;10(4):2872-2880. doi:10.21597/jist.703428
Chicago Bilen, Lokman. “Infinitesimal Paraholomorphically Projective Transformation On Cotangent Bundle With Riemannian Extension”. Journal of the Institute of Science and Technology 10, sy. 4 (Aralık 2020): 2872-80. https://doi.org/10.21597/jist.703428.
EndNote Bilen L (01 Aralık 2020) Infinitesimal Paraholomorphically Projective Transformation On Cotangent Bundle With Riemannian Extension. Journal of the Institute of Science and Technology 10 4 2872–2880.
IEEE L. Bilen, “Infinitesimal Paraholomorphically Projective Transformation On Cotangent Bundle With Riemannian Extension”, Iğdır Üniv. Fen Bil Enst. Der., c. 10, sy. 4, ss. 2872–2880, 2020, doi: 10.21597/jist.703428.
ISNAD Bilen, Lokman. “Infinitesimal Paraholomorphically Projective Transformation On Cotangent Bundle With Riemannian Extension”. Journal of the Institute of Science and Technology 10/4 (Aralık 2020), 2872-2880. https://doi.org/10.21597/jist.703428.
JAMA Bilen L. Infinitesimal Paraholomorphically Projective Transformation On Cotangent Bundle With Riemannian Extension. Iğdır Üniv. Fen Bil Enst. Der. 2020;10:2872–2880.
MLA Bilen, Lokman. “Infinitesimal Paraholomorphically Projective Transformation On Cotangent Bundle With Riemannian Extension”. Journal of the Institute of Science and Technology, c. 10, sy. 4, 2020, ss. 2872-80, doi:10.21597/jist.703428.
Vancouver Bilen L. Infinitesimal Paraholomorphically Projective Transformation On Cotangent Bundle With Riemannian Extension. Iğdır Üniv. Fen Bil Enst. Der. 2020;10(4):2872-80.