Notes on some properties of the natural Riemann extension

ocak, filiz

doi:10.31801/cfsuasmas.1067247

Notes on some properties of the natural Riemann extension

Filiz OCAK (Karadeniz Teknik Üniversitesi, Matematik Bölümü, Trabzon, Türkiye)

Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics

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Yıl: 2023 Cilt: 72 Sayı: 2 Sayfa Aralığı: 363 - 373 Metin Dili: İngilizce DOI: 10.31801/cfsuasmas.1067247 İndeks Tarihi: 29-06-2023

Notes on some properties of the natural Riemann extension

Öz:

Let $(M,nabla)$ be an $n$-dimensional differentiable manifold with a torsion-free linear connection and $T^{*}M$ its cotangent bundle. In this context we study some properties of the natural Riemann extension (M. Sekizawa (1987), O. Kowalski and M. Sekizawa (2011)) on the cotangent bundle $T^{*}M$. First, we give an alternative definition of the natural Riemann extension with respect to horizontal and vertical lifts. Secondly, we investigate metric connection for the natural Riemann extension. Finally, we present geodesics on the cotangent bundle $T^{*}M$ endowed with the natural Riemann extension.

Anahtar Kelime: Vertical and horizontal lift adapted frame geodesics natural Riemann extension cotangent bundle

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık

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APA	ocak f (2023). Notes on some properties of the natural Riemann extension. , 363 - 373. 10.31801/cfsuasmas.1067247
Chicago	ocak filiz Notes on some properties of the natural Riemann extension. (2023): 363 - 373. 10.31801/cfsuasmas.1067247
MLA	ocak filiz Notes on some properties of the natural Riemann extension. , 2023, ss.363 - 373. 10.31801/cfsuasmas.1067247
AMA	ocak f Notes on some properties of the natural Riemann extension. . 2023; 363 - 373. 10.31801/cfsuasmas.1067247
Vancouver	ocak f Notes on some properties of the natural Riemann extension. . 2023; 363 - 373. 10.31801/cfsuasmas.1067247
IEEE	ocak f "Notes on some properties of the natural Riemann extension." , ss.363 - 373, 2023. 10.31801/cfsuasmas.1067247
ISNAD	ocak, filiz. "Notes on some properties of the natural Riemann extension". (2023), 363-373. https://doi.org/10.31801/cfsuasmas.1067247

APA	ocak f (2023). Notes on some properties of the natural Riemann extension. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics, 72(2), 363 - 373. 10.31801/cfsuasmas.1067247
Chicago	ocak filiz Notes on some properties of the natural Riemann extension. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics 72, no.2 (2023): 363 - 373. 10.31801/cfsuasmas.1067247
MLA	ocak filiz Notes on some properties of the natural Riemann extension. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics, vol.72, no.2, 2023, ss.363 - 373. 10.31801/cfsuasmas.1067247
AMA	ocak f Notes on some properties of the natural Riemann extension. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics. 2023; 72(2): 363 - 373. 10.31801/cfsuasmas.1067247
Vancouver	ocak f Notes on some properties of the natural Riemann extension. Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics. 2023; 72(2): 363 - 373. 10.31801/cfsuasmas.1067247
IEEE	ocak f "Notes on some properties of the natural Riemann extension." Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics, 72, ss.363 - 373, 2023. 10.31801/cfsuasmas.1067247
ISNAD	ocak, filiz. "Notes on some properties of the natural Riemann extension". Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics 72/2 (2023), 363-373. https://doi.org/10.31801/cfsuasmas.1067247