Infinitesimal Paraholomorphically Projective Transformation On Cotangent Bundle With Riemannian Extension
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
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.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Research Article |
| Authors | |
| Submission Date | March 13, 2020 |
| Acceptance Date | June 7, 2020 |
| Publication Date | December 15, 2020 |
| Published in Issue | Year 2020 Volume: 10 Issue: 4 |