본문 바로가기
KERD
논문KCI 등재

Certain results on almost Kenmotsu manifolds with conformal Reeb foliation

2

조회

0

다운로드

0

인용

0

참고문헌

키워드

주제분류수학

초록

The object of the present paper is to study some curvature properties of almost Kenmotsu manifolds with conformal Reeb foliation. Among others it is proved that an almost Kenmotsu manifold with conformal Reeb foliation is Ricci semisymmetric if and only if it is an Einstein manifold. Finally, we study Yamabe soliton in this manifold.

Abstract

The object of the present paper is to study some curvature properties of almost Kenmotsu manifolds with conformal Reeb foliation. Among others it is proved that an almost Kenmotsu manifold with conformal Reeb foliation is Ricci semisymmetric if and only if it is an Einstein manifold. Finally, we study Yamabe soliton in this manifold.

참고문헌 (29)

  1. C. L. Bejan, "Second order parallel tensors and Ricci solitons in 3-dimensional normal paracontact geometry", Ann. Glob. Anal. Geom., 46(2), pp.117~127 (2014)[DOI]
  2. D. E. Blair, "Contact manifold in Reimannian Geometry", Lecture Notes on Mathematics, pp.509~ (1976)
  3. D. E. Blair, "Riemannian Geomatry on contact and sympletic manifolds", Progr. Math. Birkhauser (2010)
  4. D. E. Blair, "Contact metric manifolds satisfying a nullitty condition", Israel J. Math., 91(1-3), pp.189~214 (1995)[DOI]
  5. B. Chow, "Hamilton's Ricci flow", Graduate Studies in Mathematics, 77 (2006), American Mathematical Society
  6. U. C. De, "On a type of almost Kenmotsu manifolds with nullity distri-bution", Arab J. Math. Sci.
  7. U. C. De, "On <TEX>$\phi$<", TEX>-Ricci recurrent almost Kenmotsu manifolds with nullity distribution, 2016, pp.9(2), 70~79
  8. Uday Chand De, "On locally Φ-conformally symmetric almost Kenmotsu manifolds with nullity distributions", 대한수학회논문집, 32(2), pp.401~416 (2017), 대한수학회
  9. U. C. De, "On a type of Kenmotsu manifolds", J. Pure Math., 18, pp.79~83 (2001)
  10. G. Dileo, "Almost Kenmotsu manifolds and local symmetry", Bull. Belg. Math. Soc. Simon Stevin, 14(2), pp.343~354 (2007)
  11. R. S. Hamilton, "The Ricci flow on surfaces, Mathematics and General Relativity (Santa Cruz, CA, 1986)", Contemp. Math., 71, pp.237~262 (1988), Amer. Math. Soc.
  12. D. Janssens, "Almost contact structures and curvature tensors", Kodai Math J. Geom., 4(1), pp.1~27 (1981)[DOI]
  13. K. Kenmotsu, "A class of almost contact Riemannian manifolds", Tohoku Math. J., 24, pp.93~103 (1972)[DOI]
  14. K. Mandal, "Ricci solitons on almost Kenmotsu manifolds", An. Univ. Oradea Fasc. Mat., 2(2), pp.109~116 (2016)
  15. A. M. Pastore, "Almost Kenmotsu manifolds with conformal Reeb foliation", Bull. Belg. Math. Soc. Simon Stevin, 18(4), pp.655~666 (2011)
  16. G. Pitis, "Geometry of Kenmotsu manifolds" (2007), Brasov
  17. S. Sasaki, "Almost contact manifolds", Lecture Notes, Tohoku Univ., 1;2;3 (1968)
  18. P. A. Shirokov, "Constant vector fields and tensor fields of second order in Riemannian spaces", Izv. Kazan Fiz. Mat. Obshchestva Ser., 25, pp.86~114 (1925)
  19. Z. I. Szabo, "Structures theorems on Riemannian spaces satisfying R(X; Y)<TEX>${\cdot}$<", TEX>R = 0 I the local version, 1982, pp.17(4), 531~582
  20. L. Verstraelen, "Comments on pseudosymmetry in the sense of Ryszard Deszcz;Geometry and Topology of submanifolds, VI", pp.199~209 (1994), World Sci. Publishing
  21. Y. Wang, "Yamabe solitons in three dimensional kenmotsu manifolds", Bull. Belg. Math. Soc. Stenvin, 23, pp.345~355 (2016)
  22. Yaning Wang, "Gradient Ricci almost solitons on two classes of almost Kenmotsu manifolds", 대한수학회지, 53(5), pp.1101~1114 (2016), 대한수학회
  23. Y. Wang, "Gradient Ricci solitons on almost Kenmotsu manifolds", Publ. Inst. Math. (Beograd) (N.S), 98(112), pp.227~235 (2015)[DOI]
  24. Y. Wang, "Riemannian semisymmetric almost Kenmotsu manifolds and nul-lity distributions", Ann. Polon. Math., 112(1), pp.37~46 (2014)[DOI]
  25. Y. Wang, "Locally symmetric CR-integrable almost Kenmotsu manifolds", Mediterr. J. Math., 12(1), pp.159~171 (2015)[DOI]
  26. Y. Wang, "On <TEX>$\phi$<", TEX>-recurrent almost Kenmotsu manifolds, 2015, pp.42(1), 65~77
  27. Y. Wang, "Ricci solitons on three dimensional <TEX>$\eta$<", TEX>-Einstein almost Kenmotsu manifolds, 2015, pp.19(1), 91~100
  28. Y. Wang, "On almost Kenmotsu manifolds satisfying some nullity distributions", Proc. Nat. Acad. Sci. India Sect. A, 86(3), pp.347~353 (2016)[DOI]
  29. Y. Wang, "Curvature properties of almost Kenmotsu manifolds with gen-eralized nullity conditions", Filomat, 30(14), pp.3807~3816 (2016)[DOI]

관련 논문AI추천

이 간행물의 다른 논문 (26건)