On the Class of Einstein Exponential-Type Finsler Metrics

Автор(и)

  • Akbar Tayebi
  • Ali Nankali University of Qom, Department of Mathematics, Faculty of Science, Qom, Iran
  • Behzad Najafi Amirkabir University, Department of Mathematics and Computer Sciences, Tehran, Iran

DOI:

https://doi.org/10.15407/mag14.01.100

Ключові слова:

ейнштейнова метрика, метрика unicorn, експоненцiальна метрика.

Анотація

У статтi вивчається спецiальний клас фiнслерових метрик, що називаються (α, β)-метриками, якi визначаються формулою F = αφ(s), де α - рiманова метрика, а β - 1-форма. Спочатку ми показуємо, що клас майже регулярних метрик, отриманий Шеном, є ейнштейновим тодi i тiльки тодi, коли вiн зводиться до класу метрик Бервальда. В цьому випадку метрики є Рiччi-пласкими. Потiм ми доводимо, що експоненцiальна метрика є ейнштейновою тодi i тiльки тодi, коли вона Рiччi-пласка.

2010:53B40, 53C60.

Посилання

H. Akbar-Zadeh, Generalized Einstein manifolds, J. Geom. Phys, 17 (1995), 342– 380. https://doi.org/10.1016/0393-0440(94)00052-2

H. Akbar-Zadeh, Geometry of Einstein manifolds, C.R. Acad. Sci. Paris 339 (2004), 125–130. https://doi.org/10.1016/j.crma.2004.05.002

G.S. Asanov, Finsleroid–Finsler space with Berwald and Landsberg conditions, arxiv.org/abs/math/0603472.

V. Balan, On the generalized Einstein Yang–Mills equations, Publ. Math. Debrecen 43 (1993), 272–282.

D. Bao, Unicorns in Finsler geometry, Proceedings of the 40th Symposium on Finsler geometry, Sapporo, Japan, 2005, 19–27.

D. Bao, On two curvature-driven problems in Riemann–Finsler geometry, Adv. Stud. Pure. Math. 48 (2007), 19–71.

D. Bao and C. Robles, Ricci and flag curvatures in Finsler geometry, in “A Sampler of Finsler Geometry”, Math. Sci. Res. Inst. Publ., 50, Cambridge University Press, Cambridge, 2004, 197–259.

R.L. Bryant, Finsler surfaces with prescribed curvature conditions, unpublished preprint (part of his Aisenstadt lectures), 1995.

X. Cheng, Z. Shen and Y. Tian, A class of Einstein (α, β)-metrics, Israel J. Math. 192 (2012), 221–249. https://doi.org/10.1007/s11856-012-0036-x

B. Najafi and A. Tayebi, On a family of Einstein–Randers metrics, Int. J. Geom. Methods Mod. Phys. 8 (2011), 1021–1029. https://doi.org/10.1142/S021988781100552X

L.-I. Pişcoran and V. N. Mishra, S-curvature for a new class of (α, β)-metrics, Rev. R. Acad. Cienc. Exactas Fı́s. Nat. Ser. A Math. RACSAM 111 (2017), 1187—1200. https://doi.org/10.1007/s13398-016-0358-3

Z. Shen, On projectively flat (α, β)-metrics, Canad. Math. Bull. 52 (2009), 132–144. https://doi.org/10.4153/CMB-2009-016-2

Z. Shen, On a class of Landsberg metrics in Finsler geometry, Canadian. J. Math. 61 (2009), 1357–1374. https://doi.org/10.4153/CJM-2009-064-9

Z. Shen and C. Yu, On Einstein square metrics, arxiv.org/abs/1209.3876.

Z. Shen and C. Yu, On a class of Einstein–Finsler metrics, Internat. J. Math. 25 (2014) 1450030, 18 pp. https://doi.org/10.1142/S0129167X1450030X

A. Tayebi, On the class of generalized Landsberg manifolds, Period. Math. Hungar. 72 (2016), 29–36. https://doi.org/10.1007/s10998-015-0108-x

A. Tayebi and A. Alipour, On distance functions induced by Finsler metrics, Publ. Math. Debrecen 90 (2017), 333–357. https://doi.org/10.5486/PMD.2017.7505

A. Tayebi and M. Barzegari, Generalized Berwald spaces with (α, β)-metrics, Indag. Math. (N.S.) 27 (2016), 670–683. https://doi.org/10.1016/j.indag.2016.01.002

A. Tayebi and A. Nankali, On generalized Einstein–Randers metrics, Int. J. Geom. Methods Mod. Phys. 12 (2015), 1550105, 14 pp.

A. Tayebi and H. Sadeghi, On generalized Douglas–Weyl (α, β)-metrics, Acta Math. Sin. (Engl. Ser.) 31 (2015), 1611–1620. https://doi.org/10.1007/s10114-015-3418-2

A. Tayebi and H. Sadeghi, Generalized P-reducible (α, β)-metrics with vanishing S-curvature, Ann. Polon. Math. 114 (2015), 67–79. https://doi.org/10.4064/ap114-1-5

A. Tayebi and M. Shahbazi Nia, A new class of projectively flat Finsler metrics with constant flag curvature K = 1, Differential Geom. Appl. 41 (2015) 123–133. https://doi.org/10.1016/j.difgeo.2015.05.003

A. Tayebi and T. Tabatabeifar, Dougals–Randers manifolds with vanishing stretch tensor, Publ. Math. Debrecen 86 (2015), 423–432.

A. Tayebi and T. Tabatabeifar, Unicorn metrics with almost vanishing H- and Ξcurvatures, Turkish J. Math. 41 (2017), 998–1008. https://doi.org/10.3906/mat-1606-35

Y. Yu and Y. You, Projectively flat exponential Finsler metrics, J. Zhejiang Univ. Sci. A 7 (2006), 1068–1076. https://doi.org/10.1631/jzus.2006.A2097

Downloads

Опубліковано

2018-06-20

Як цитувати

(1)
Tayebi, A.; Nankali, A.; Najafi, B. On the Class of Einstein Exponential-Type Finsler Metrics. J. Math. Phys. Anal. Geom. 2018, 14, 100-114.

Номер

Розділ

Статті

Завантаження

Дані завантаження ще не доступні.