본문 바로가기
KERD
논문KCI 등재

Riemannian manifolds with a semi-symmetric metric $P$-connection

이재원|Sudhakar Kr Chaubey|Sunil Kr Yadav
대한수학회 (The Korean Mathematical Society)|2019.07|대한수학회지 (Journal of the KMS)|제56권 제4호|pp. 1113-1129|DOI 10.4134/JKMS.j180642

1

조회

0

다운로드

3

인용

0

참고문헌

키워드

Ricci solitonssemi-symmetric metric connectionsymmetric spacessecond order parallel tensorsRiemannian manifoldsdifferent curvature tensors
주제분류수학

초록

We define a class of semi-symmetric metric connection on a Riemannian manifold for which the conformal, the projective, the concircular, the quasi conformal and the $m$-projective curvature tensors are invariant. We also study the properties of semisymmetric, Ricci semisymmetric and Eisenhart problems for solving second order parallel symmetric and skew-symmetric tensors on the Riemannian manifolds equipped with a semi-symmetric metric $P$-connection.

Abstract

We define a class of semi-symmetric metric connection on a Riemannian manifold for which the conformal, the projective, the concircular, the quasi conformal and the $m$-projective curvature tensors are invariant. We also study the properties of semisymmetric, Ricci semisymmetric and Eisenhart problems for solving second order parallel symmetric and skew-symmetric tensors on the Riemannian manifolds equipped with a semi-symmetric metric $P$-connection.

참고문헌 (35)

  1. B. Barua, "Some properties of semisymmetric metric connection in a Riemannian manifold", Indian J. Pure Appl. Math, 16(7), pp.736~740 (1985)
  2. C. Calin, "From the Eisenhart problem to Ricci solitons in f-Kenmotsu manifolds", Bull. Malays. Math. Sci. Soc, 33(3), pp.361~368 (2010)
  3. S. K. Chaubey, "Certain results on N(k)-quasi Einstein manifolds", Afrika Matematika, 30(1-2), pp.113~127 (2019), Springer Science and Business Media LLC[DOI]
  4. S. K. Chaubey, "Semi-symmetric metric T-connection in an almost contact metric manifold", Int. Math. Forum, 5(21-24), pp.1121~1129 (2010)
  5. S. K. Chaubey, "On the m-projective curvature tensor of a Kenmotsu manifold", Differ. Geom. Dyn. Syst, 12, pp.52~60 (2010)
  6. S. K. Chaubey, "On a semi-symmetric non-metric connection", Filomat, 26(2), pp.269~275 (2012)
  7. Sudhakar Kumar Chaubey, "On $3$-dimensional Lorentzian concircular structure manifolds", 대한수학회논문집, 34(1), pp.303~319 (2019), 대한수학회[DOI]
  8. S. K. Chaubey, "Study of Kenmotsu manifolds with semi-symmetric metric connection", Universal J. Math. Appl, 1(2), pp.89~97 (2018)
  9. M. Crasmareanu, "Parallel tensors and Ricci solitons in N(k)-quasi Einstein manifolds", Indian J. Pure Appl. Math, 43(4), pp.359~369 (2012)
  10. U. C. De, "On a type of semi-symmetric metric connection on an almost contact metric manifold", Facta Univ. Ser. Math. Inform, 16, pp.87~96 (2001)
  11. L. P. Eisenhart, "Symmetric tensors of the second order whose first covariant derivatives are zero", Trans. Amer. Math. Soc, 25(2), pp.297~306 (1923)
  12. A. Friedmann, "¨Uber die Geometrie der halbsymmetrischen ¨Ubertragungen", Math. Z, 21(1), pp.211~223 (1924)
  13. R. S. Hamilton, "The Ricci flow on surfaces", Mathematics and general relativity, Contemp. Math, pp.237~262 (1988), Amer. Math. Soc
  14. H. A. Hayden, "Sub-spaces of a space with torsion", Proc. London Math. Soc, 34(1), pp.27~50 (1932)
  15. 진대호, "HALF LIGHTLIKE SUBMANIFOLDS OF A SEMI-RIEMANNIAN SPACE FORM WITH A SEMI-SYMMETRIC NON-METRIC CONNECTION", 순수 및 응용수학, 21(1), pp.39~50 (2014), 한국수학교육학회
  16. D. H. Jin, "Einstein half lightlike submanifolds of a Lorentzian space form with a semi-symmetric metric connection", Quaest. Math, 37(4), pp.485~505 (2014)
  17. H. Levy, "Symmetric tensors of the second order whose covariant derivatives vanish", Ann. of Math, 27(2), pp.91~98 (1925)
  18. R. S. Mishra, "Semi-symmetric metric connections in an almost contact manifold", Indian J. Pure Appl. Math, 9(6), pp.570~580 (1978)
  19. C. Murathan, "Riemannian manifolds with a semi-symmetric metric connection satisfying some semisymmetry conditions", Proc. Est. Acad. Sci, 57(4), pp.210~216 (2008)
  20. E. Pak, "On the pseudo-Riemannian spaces", J. Korean Math. Soc, 6, pp.23~31 (1969)
  21. G. P. Pokhariyal, "Curvature tensors and their relativistic significance. II", Yokohama Math. J, 19(2), pp.97~103 (1971)
  22. G. P. Pokhariyal, "Ricci solitons on trans-Sasakian manifolds", Differ. Geom. Dyn. Syst, 20, pp.138~158 (2018)
  23. R. Sharma, "Second order parallel tensor in real and complex space forms", Internat. J. Math. Math. Sci, 12(4), pp.787~790 (1989)
  24. R. Sharma, "Second order parallel tensors on contact manifolds", Algebras Groups Geom, 7(2), pp.145~152 (1990)
  25. R. Sharma, "Second order parallel tensors on contact manifolds. II", C. R. Math. Rep. Acad. Sci. Canada, 13(6), pp.259~264 (1991)
  26. R. Sharma, "On the curvature of contact metric manifolds", J. Geom, 53(1-2), pp.179~190 (1995)
  27. Z. I. Szabo, "Structure theorems on Riemannian spaces satisfying R(X, Y ) · R = 0. I. The local version", J. Differential Geom, 17(4), pp.531~582 (1982)[DOI]
  28. Z. I. Szabo, "Structure theorems on Riemannian spaces satisfying R(X, Y )·R = 0. II. Global versions", Geom. Dedicata, 19(1), pp.65~108 (1985)
  29. L. Tam´assy, "On weak symmetries of Einstein and Sasakian manifolds, Tensor (N.S.)", Commemoration, 53(1), pp.140~148 (1993)
  30. H. Weyl, "Reine Infinitesimalgeometrie", Math. Z, 2(3-4), pp.384~411 (1918)
  31. K. Yano, "On semi-symmetric metric connection", Rev. Roumaine Math. Pures Appl, 15, pp.1579~1586 (1970)
  32. K. Yano, "Concircular geometry. I. Concircular transformations", Proc. Imp. Acad. Tokyo, 16, pp.195~200 (1940)
  33. K. Yano, "Curvature and Betti Numbers" (1953), Princeton University Press
  34. K. Yano, "Riemannian manifolds admitting a conformal transformation group", J. Differential Geometry, 2, pp.161~184 (1968)
  35. F. Zengin, "Some vector fields on a Riemannian manifold with semi-symmetric metric connection", Bull. Iranian Math. Soc, 38(2), pp.479~490 (2012)

관련 논문AI추천

On a Type of Semi-Symmetric Non-Metric Connection on Riemannian ManifoldsAjit Barman경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2015 · 제55권 제3호On a type of semi-symmetric non metric connection in Lorentzian para-Sasakian manifoldE. Yasar장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2011 · 제14권 제2호ON A SEMI-SYMMETRIC METRIC CONNECTION IN AN (ε)-KENMOTSU MANIFOLDGiteshwari Pandey, Kiran Tiwari, Ram Nawal Singh, Shravan Kumar Pandey대한수학회 · 대한수학회논문집2014 · 제29권 제2호Geometry of a semi-symmetric recurrent metric connection김재만대한수학회 · 대한수학회논문집2023 · 제38권 제4호On Concircular Curvature Tensor with respect to the Semisymmetric Non-metric Connection in a Kenmotsu ManifoldAbdul Haseeb경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2016 · 제56권 제3호SEMI-RIEMANNIAN SUBMANIFOLDS OF A SEMI-RIEMANNIAN MANIFOLD WITH A SEMI-SYMMETRIC NON-METRIC CONNECTIONAhmet Yucesan, Erol Yasar대한수학회 · 대한수학회논문집2012 · 제27권 제4호

이 간행물의 다른 논문 (13건)

On a class of quasilinear elliptic equation with indefinite weights on graphsGuoqing Zhang, Shoudong Manpp. 857-867A characterization of class groups via sets of lengthsAlfred Geroldinger, Wolfgang Alexander Schmidpp. 869-915Homogeneity and symmetry on almost Kenmotsu $3$-manifoldsYaning Wangpp. 917-934Limit theorems for Hawkes processes with uniform immigrants설영수pp. 935-946Shifted tableau switchings and shifted Littlewood-Richardson coefficients최승일, 오영탁, 남선영pp. 947-984
원문 보기