Araştırma Makalesi
Yıl 2023,
Sayı: 42, 1 - 7, 31.03.2023
Öz
Kaynakça
- S. Sasaki, On the Differential Geometry of Tangent Bundles of Riemannian Manifolds, Tohoku Mathematical Journal 10 (1958) 338–358.
- E. Musso, F. Tricerri, Riemannian Metrics on Tangent Bundles, Annali di Matematica Pura ed Applicata 150 (4) (1988) 1–19.
- B. V. Zayatuev, On Geometry of Tangent Hermitian Surface, Webs and Quasigroups T. S. U. (1995) 139–143.
- L. Belarbi, H. El Hendi, Geometry of Twisted Sasaki Metric, Journal of Geometry and Symmetry in Physics 53 (2019) 1–19.
- A. Zagane, M. Djaa, Geometry of Mus-Sasaki Metric, Communications in Mathematics 26 (2) (2018) 113–126.
- J. Wang, Y. Wang, On the Geometry of Tangent Bundles with the Rescaled Metric (2011), https://arxiv.org/abs/1104.5584.
- M. Benyounes, M., E. Loubeau, C. M. Wood, The Geometry of Generalised Cheeger-Gromoll Metrics, Tokyo Journal of Mathematics 32 (2009) 1–26.
- A. Gezer, M. Altunba¸s, Some Notes Concerning Riemannian Metrics of Cheeger Gromoll Type, Journal of Mathematical Analysis and Applications 396 (1) (2012) 119–132.
- F. Latti, M. Djaa, On the Geometry of the Mus-Cheeger-Gromoll Metric, Bulletin Transilvania University Brasov Series III 64 (2) (2022) 121–138.
- A. Gezer, L. Bilen, On Infinitesimal Conformal Transformations of the Tangent Bundles with Respect to the Cheeger-Gromoll Metric, Analele Stiintifice ale Universitatii Ovidius Constanta 20 (1) (2012) 113–128.
- I. Hasegawa, K. Yamauchi, Infinitesimal Conformal Transformations on Tangent Bundles with the Lift Metric I+II, Scientiae Mathematicae Japonicae 57 (1) (2003) 129–137.
- A. Heydari, E. Peyghan, A Characterization of the Infinitesimal Conformal Transformations on Tangent Bundles, Bulletin of the Iranian Mathematical Society 34 (2) (2008) 59–70.
- K. Yamauchi, On Infinitesimal Conformal Transformations of the Tangent Bundles with the Metric I+III over Riemannian Manifold, Annals of Reprints of Asahikawa Medical College 16 (1995) 1–6.
- K. Yamauchi, On Infinitesimal Conformal Transformations of the Tangent Bundles over Riemannian Manifolds, Annals of Reprints of Asahikawa Medical College 15 (1994) 1–10.
- S. Amari, Differential-Geometrical Methods in Statistics, Vol. 28 of Lecture Notes in Statistics, Springer, New York, 1985.
- S. L. Lauritzen, Statistical Manifolds, in: S. S. Gupta (Ed.), Differential Geometry in Statistical Inference, Vol. 10 of Lecture Notes-Monograph Series, Institute of Mathematical Statistics, Hayward, 1987, Ch. 4, pp. 163–216.
- V. Balan, E. Peyghan, E. Sharahi, Statistical Structures on the Tangent Bundle of a Statistical Manifold with Sasaki Metric, Hacettepe Journal of Mathematics and Statistics 49 (1) (2020) 120–135.
- E. Peyghan, D. Seifipour, A. Gezer, Statistical Structures on Tangent Bundles and Lie Groups, Hacettepe Journal of Mathematics and Statistics 50 (2021) 1140–1154.
- E. Peyghan, D. Seifipour, A. Blaga, On the Geometry of Lift Metrics and Lift Connections on the Tangent Bundle, Turkish Journal of Mathematics 46 (6) (2022) 2335–2352.
- K. Yano, S. Ishihara, Tangent and Cotangent Bundles: Differential Geometry, Vol. 16 of A Series of Monographs and Textbooks, Marcel Dekker, New York, 1973.
- L. Belarbi, H. El Hendi, F. Latti, On the Geometry of the Tangent Bundle with Vertical Rescaled Generalized Cheeger-Gromoll Metric, Bulletin of Transilvania University of Brasov. Series III: Mathematics and Computer Science 12 (61) (2019) 247–264.
Yıl 2023,
Sayı: 42, 1 - 7, 31.03.2023
Öz
In this paper, we first show that the complete lift $U^{c}$ to $TM$ of a vector field $U$ on $M$ is an infinitesimal fiber-preserving conformal transformation if and only if $U$ is an infinitesimal homothetic transformation of $(M,g)$. Here, $(M, g)$ is a Riemannian manifold and $TM$ is its tangent bundle with a Mus-Cheeger-Gromoll type metric $\tilde{g}$. Secondly, we search for some conditions under which $\left(\overset{h}{\nabla},\tilde{g}\right)$ is a Codazzi pair on $TM$ when $(\nabla, g)$ is a Codazzi pair on $M$ where $\overset{h}{\nabla}$ is the horizontal lift of a linear connection $\nabla$ on $M$. We finally discuss the need for further research.
Anahtar Kelimeler
Codazzi pair infinitesimal fiber-preserving conformal transformation infinitesimal homothetic transformation Mus-Cheeger-Gromoll type metric tangent bundle
Kaynakça
- S. Sasaki, On the Differential Geometry of Tangent Bundles of Riemannian Manifolds, Tohoku Mathematical Journal 10 (1958) 338–358.
- E. Musso, F. Tricerri, Riemannian Metrics on Tangent Bundles, Annali di Matematica Pura ed Applicata 150 (4) (1988) 1–19.
- B. V. Zayatuev, On Geometry of Tangent Hermitian Surface, Webs and Quasigroups T. S. U. (1995) 139–143.
- L. Belarbi, H. El Hendi, Geometry of Twisted Sasaki Metric, Journal of Geometry and Symmetry in Physics 53 (2019) 1–19.
- A. Zagane, M. Djaa, Geometry of Mus-Sasaki Metric, Communications in Mathematics 26 (2) (2018) 113–126.
- J. Wang, Y. Wang, On the Geometry of Tangent Bundles with the Rescaled Metric (2011), https://arxiv.org/abs/1104.5584.
- M. Benyounes, M., E. Loubeau, C. M. Wood, The Geometry of Generalised Cheeger-Gromoll Metrics, Tokyo Journal of Mathematics 32 (2009) 1–26.
- A. Gezer, M. Altunba¸s, Some Notes Concerning Riemannian Metrics of Cheeger Gromoll Type, Journal of Mathematical Analysis and Applications 396 (1) (2012) 119–132.
- F. Latti, M. Djaa, On the Geometry of the Mus-Cheeger-Gromoll Metric, Bulletin Transilvania University Brasov Series III 64 (2) (2022) 121–138.
- A. Gezer, L. Bilen, On Infinitesimal Conformal Transformations of the Tangent Bundles with Respect to the Cheeger-Gromoll Metric, Analele Stiintifice ale Universitatii Ovidius Constanta 20 (1) (2012) 113–128.
- I. Hasegawa, K. Yamauchi, Infinitesimal Conformal Transformations on Tangent Bundles with the Lift Metric I+II, Scientiae Mathematicae Japonicae 57 (1) (2003) 129–137.
- A. Heydari, E. Peyghan, A Characterization of the Infinitesimal Conformal Transformations on Tangent Bundles, Bulletin of the Iranian Mathematical Society 34 (2) (2008) 59–70.
- K. Yamauchi, On Infinitesimal Conformal Transformations of the Tangent Bundles with the Metric I+III over Riemannian Manifold, Annals of Reprints of Asahikawa Medical College 16 (1995) 1–6.
- K. Yamauchi, On Infinitesimal Conformal Transformations of the Tangent Bundles over Riemannian Manifolds, Annals of Reprints of Asahikawa Medical College 15 (1994) 1–10.
- S. Amari, Differential-Geometrical Methods in Statistics, Vol. 28 of Lecture Notes in Statistics, Springer, New York, 1985.
- S. L. Lauritzen, Statistical Manifolds, in: S. S. Gupta (Ed.), Differential Geometry in Statistical Inference, Vol. 10 of Lecture Notes-Monograph Series, Institute of Mathematical Statistics, Hayward, 1987, Ch. 4, pp. 163–216.
- V. Balan, E. Peyghan, E. Sharahi, Statistical Structures on the Tangent Bundle of a Statistical Manifold with Sasaki Metric, Hacettepe Journal of Mathematics and Statistics 49 (1) (2020) 120–135.
- E. Peyghan, D. Seifipour, A. Gezer, Statistical Structures on Tangent Bundles and Lie Groups, Hacettepe Journal of Mathematics and Statistics 50 (2021) 1140–1154.
- E. Peyghan, D. Seifipour, A. Blaga, On the Geometry of Lift Metrics and Lift Connections on the Tangent Bundle, Turkish Journal of Mathematics 46 (6) (2022) 2335–2352.
- K. Yano, S. Ishihara, Tangent and Cotangent Bundles: Differential Geometry, Vol. 16 of A Series of Monographs and Textbooks, Marcel Dekker, New York, 1973.
- L. Belarbi, H. El Hendi, F. Latti, On the Geometry of the Tangent Bundle with Vertical Rescaled Generalized Cheeger-Gromoll Metric, Bulletin of Transilvania University of Brasov. Series III: Mathematics and Computer Science 12 (61) (2019) 247–264.
Toplam 21 adet kaynakça vardır.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Matematik |
| Bölüm | Araştırma Makalesi |
| Yazarlar | |
| Yayımlanma Tarihi | 31 Mart 2023 |
| Gönderilme Tarihi | 25 Ağustos 2022 |
| Yayımlandığı Sayı | Yıl 2023 Sayı: 42 |
Kaynak Göster
- Makale Dosyaları