Moreover, if 𝑇∗𝑀 be admits a non-affine infinitesimal paraholomorphically projective transformation, than 𝑀 and 𝑇∗𝑀 are locally flat.
📌 3 Maddede Bu Makale
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Amaç & Hipotez: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.
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Temel Bulgular & Veri: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.
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Sonuç & Katkı:Moreover, if 𝑇∗𝑀 be admits a non-affine infinitesimal paraholomorphically projective transformation, than 𝑀 and 𝑇∗𝑀 are locally flat.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:paraholomorphically projective transformation · almost paracomplex structure · Riemannian extension
Özet
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.
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.
Bilen, L. (2020). Infinitesimal Paraholomorphically Projective Transformation On Cotangent Bundle With Riemannian Extension. Iğdır Üniversitesi Fen Bilimleri Enstitüsü Dergisi, Cilt: 10 Sayı: 4, 2872–2880. https://doi.org/10.21597/jist.703428
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.