본문 바로가기
KERD
논문KCI 등재

Four-dimensional Naturally Reductive Pseudo-Riemannian Homogeneous Spaces

Barbara De Leo
경북대학교 자연과학대학 수학과|2012.03|Kyungpook Mathematical Journal|제52권 제1호|pp. 1-11

2

조회

0

다운로드

0

인용

0

참고문헌

키워드

Pseudo-Riemannian metricshomogeneous manifoldsnaturally reductive spaces
주제분류수학

초록

Our attention is turned to four-dimensional pseudo-Riemannian naturally reductive homogeneous spaces. In particular, our study leads to a complete classification of them.

Abstract

Our attention is turned to four-dimensional pseudo-Riemannian naturally reductive homogeneous spaces. In particular, our study leads to a complete classification of them.

참고문헌 (21)

  1. W. Ambrose, "On homogeneous Riemannian manifolds", Duke Math. J., 25, pp.647~669 (1958)
  2. G. Calvaruso, "Homogeneous geodesics of non-unimodular Lorentzian Lie groups and naturally reductive Lorentzian spaces in dimension three", Adv. Geom, 8, pp.473~489 (2008)
  3. L. A Cordero, "Left-invariant Lorentzian metrics on 3-dimensional Lie groups", Rend. Mat. Appl., 17(7), pp.129~155 (1997)
  4. J. E. D’Atri, "Geodesic spheres and symmetries in naturally reductive homogeneous spaces", Michigan Math. J., 22, pp.71~76 (1975)
  5. J. E. D’Atri, "Naturally reductive metrics and Einstein metrics on compact Lie groups", Mem. Amer. Math. Soc, 18, pp.215~ (1979)
  6. B. De Leo, "Special Homogeneous structures on pseudo- Riemannian manifolds", JP Journal of Geometry and Topology, 8(3), pp.203~228 (2008)
  7. P. M. Gadea, "Homogeneous pseudo-Riemannian structures and homogeneous almost para-Hermitian structures, Houston", J. Math., 18(3), pp.449~465 (1992)
  8. P. M. Gadea, "Reductive homogeneous pseudo-Riemannian manifolds", Mh. Math., 124, pp.17~34 (1997)
  9. N. Haouari, "Three-dimensional naturally reductive homogeneous Lorentzian manifolds", Mediterranean J. Math., 5, pp.113~131 (2008)
  10. S. Kobayashi, "Foundations of differential geometry, II" (1969), Intersciences Publ.
  11. O. Kowalski, "Spaces with volume-preserving symmetries and related classes of Riemannian manifolds", Rend. Semin. Mat. Univ. Politec. Torino, Fascicolo Speciale, pp.131~158 (1983)
  12. O. Kowalski, "Generalized symmetric spaces, Lectures Notes in Math." (1980), Springer- Verlag
  13. O. Kowalski, "Four-dimensional naturally reductive homogeneous spaces", Rend. Sem. Mat. Torino, Fasc. Speciale, pp.223~232 (1985)
  14. J. Milnor, "Curvature of left invariant metrics on Lie groups", Adv. Math., 21, pp.293~329 (1976)
  15. K. Nomizu, "Invariant affine connection on homogeneous spaces", Amer. J. Math., 76, pp.33~65 (1954)
  16. B. O’Neill, "Semi-Riemannian Geometry" (1983), Academic Press
  17. F. Tricerri, "Homogeneous structures on Riemannian manifolds, In London Math. Soc. Lect. Notes 83" (1983), Cambridge Univ. Press
  18. F. Tricerri, "Geodesic spheres and naturally reductive homogeneous spaces" (1985), Riv. Mat. Univ. Parma
  19. H. Wu, "On the de Rham decomposition theorem", Illinois J. Math., 8, pp.291~311 (1964)
  20. H. Wu, "Decomposition of Riemannian manifolds", Bull. Amer. Math. Soc., 70, pp.610~617 (1964)
  21. H. Wu, "Holonomy groups of indefinite metrics", Pacific J. Math., 20, pp.351~392 (1967)

관련 논문AI추천

Homogeneous structures on four-dimensional Lorentzian Damek-Ricci spacesAssia Mostefaoui, Noura Sidhoumi대한수학회 · 대한수학회논문집2023 · 제38권 제1호Totally geodesic and parallel hypersurfaces of 4-dimensional Lorentzian nilpotent Lie groupsJinguo Jiang, Yanni Yang대한수학회 · 대한수학회보2025 · 제62권 제4호Classification of homogeneous structures on 4-dimensional nilpotent Lie groupsRabea Taleb, Wafaa Batat대한수학회 · 대한수학회지2025 · 제62권 제1호SEMI-RIEMANNIAN MANIFOLDS WITH HOMOGENEOUS GEODESICS홍성관영남수학회 · East Asian Mathematical Journal2023 · 제39권 제1호On homogeneous square Einstein metricsShaoqiang Deng, Xingda Liu대한수학회 · 대한수학회보2017 · 제54권 제3호Homogeneity and symmetry on almost Kenmotsu $3$-manifoldsYaning Wang대한수학회 · 대한수학회지2019 · 제56권 제4호

이 간행물의 다른 논문 (9건)

Five Cycles are Highly Ramsey Infinite시거스, 마크 할버pp. 13-20On Certain Class of Multivalent Functions Involving the Cho-Kwon-Srivastava OperatorJamal Mohammad Shenanpp. 21-32On a Certain Integral OperatorSaurabh Porwal, Muhammed Kamal Aoufpp. 33-38Further Results about the Normal Family of Meromorphic Functions and Shared SetsJianming Qi, Linlin Zhou, Guowei Zhangpp. 39-47C-parallel Mean Curvature Vector Fields along Slant Curvesin Sasakian 3-manifolds이지은, 이현진, 서영진pp. 49-59
원문 보기