آمار

تعداد نشریات30
تعداد شماره‌ها434
تعداد مقالات3,802
تعداد مشاهده مقاله6,065,427
تعداد دریافت فایل اصل مقاله4,172,722
Seifipour, Davood. (1401). On the spectral geometry of 4-dimensional Lorentzian Lie group. سامانه مدیریت نشریات علمی, 3(2), 99-118. doi: 10.22098/jfga.2022.11917.1080
Davood Seifipour. "On the spectral geometry of 4-dimensional Lorentzian Lie group". سامانه مدیریت نشریات علمی, 3, 2, 1401, 99-118. doi: 10.22098/jfga.2022.11917.1080
Seifipour, Davood. (1401). 'On the spectral geometry of 4-dimensional Lorentzian Lie group', سامانه مدیریت نشریات علمی, 3(2), pp. 99-118. doi: 10.22098/jfga.2022.11917.1080
Seifipour, Davood. On the spectral geometry of 4-dimensional Lorentzian Lie group. سامانه مدیریت نشریات علمی, 1401; 3(2): 99-118. doi: 10.22098/jfga.2022.11917.1080

On the spectral geometry of 4-dimensional Lorentzian Lie group

Journal of Finsler Geometry and its Applications
دوره 3، شماره 2، اسفند 2022، صفحه 99-118    اصل مقاله (210.36 K)
نوع مقاله: Original Article
شناسه دیجیتال (DOI): 10.22098/jfga.2022.11917.1080
نویسنده
Davood Seifipour*
Department of Mathematics, Abadan Branch, Islamic Azad University, Abadan, Iran
چکیده
The main focus of this paper is concern to the study on the point-wise Osserman structure on 4-dimensional Lorentzian Lie group. In this paper we study on the spectrum of the Jacobi operator and spectrum of the skew-symmetric curvature operator on the non-abelian 4-dimensional Lie group G, whenever G equipped with an orthonormal left invariant pseudo-Riemannian metric g of signature (-;+;+; +), i.e, Lorentzian metric, where e1 is a unit time-like vector. The Lie algebra structure in dimension four has key role in our investigation, also in this case we study on the classification of 1-Stein and mixed IP spaces. At the end we show that G does not admit any space form and Einstein structures.
کلیدواژه‌ها
Codazzi space؛ statistical manifold؛ Lie group
مراجع
  • 1. D. Alekseevsky, N. Blazic, N.Bokan, Z. Rakic, Self-duality and pointwise Osserman
    spaces, Arch. Math. (Brno), 35, (1999), 193-201.
  • 2. N. Blazic, N. Bokan and P. Gilkey, A note on Osserman Lorentzian manifolds, Bull.
    London Math. Soc. 29 (1997), 227-230. MR 97m:5311.
  • 3. N. Blazic, N. Bokan and P. Gilkey and Z.Rakic, pseudo-Riemannian Osserman manifolds, (preprint 1997).
  • 4. M. Brozos-Vazquez, p. Gilkey and S. Nikcevic, Jacobi-Tsankov manifolds which are not
    2-step nilpotent, arxiv: math/ 0609565v1 [math DG] 20 sep 2006.
  • 5. E. Garcia-Ro, D. Kupeli, and R. Vazquez-Lorenzo, Osserman Manifolds in SemiRiemannian Geometry, Lecture notes in Mathematics, Springer Verlag, (2002), ISBN 3-540-43144-6.
  • 6. P. Gilkey, Geometric Properties of natural operators Defined by the Riemannian curvature Tensor, World Scientific Publishing Co., Inc., River Edge, NJ, 2001.
  • 7. P. Gilkey. The Geometry of Curvature Homogeneous Pseudo-Riemmannian Manifolds,
    Advanced Texts in Mathematics, 2 Imperial College Press, London, 2007.
  • 8. P. Gilkey, R. Ivanova, and T. Zhang, Szabo Osserman IP Pseudo-Riemannian manifolds,
    arXiv: math/ 0205085v1 [math. DG] 8 may 2002.
  • 9. G. M. Mubarakzyanov, On solvable Lie algebras, Izv. Vys. Ucheb. Zaved. Matematika
    (in Russian), 1(32), (1963), 114–123.
  • 10. B. O”Neil, Semi-Riemannian Geometry with application to Relativity, Academic press,
    New york, 1983.
  • 11. I. Polterovich, D. A. Sher, Heat invariants of the steklov problem, the Journal of Geometric Analysis 25, 2 (2015), 924-950.
  • 12. F. W. Warner, Foundations of differentiable manifolds and Lie groups, Scott-Foresman,
    Glenview, Illinois, 1971.
  • 13. Y. Wang, M. Ben-Chen, I. Polterovich, J. solomon, steklov spectral geometry for extrinsic
    shape analysis. arXiv: 1707.07070 (2017)
آمار
تعداد مشاهده مقاله: 267
تعداد دریافت فایل اصل مقاله: 382


سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب