Research Article
BibTex RIS Cite

Infinitesimal Paraholomorphically Projective Transformation On Cotangent Bundle With Riemannian Extension

Year 2020, , 2872 - 2880, 15.12.2020

Lokman Bilen

https://doi.org/10.21597/jist.703428

Abstract

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.

Keywords

paraholomorphically projective transformation almost paracomplex structure Riemannian extension adapted frame

References

  • 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

Year 2020, , 2872 - 2880, 15.12.2020

Lokman Bilen

https://doi.org/10.21597/jist.703428

Abstract

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.

Keywords

Paraholomorfically projective transformation almost paracomplex structure Riemannian extension adapted frame

References

  • 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.
There are 14 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Matematik / Mathematics
Authors

Lokman Bilen 0000-0001-8240-5359

Publication Date December 15, 2020
Submission Date March 13, 2020
Acceptance Date June 7, 2020
Published in Issue Year 2020

Cite

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. December 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, no. 4 (December 2020): 2872-80. https://doi.org/10.21597/jist.703428.
EndNote Bilen L (December 1, 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., vol. 10, no. 4, pp. 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 (December 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, vol. 10, no. 4, 2020, pp. 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.