A CLASSIFICATION OF (κ, μ)-CONTACT METRIC MANIFOLDS
3
조회
0
다운로드
4
인용
0
참고문헌
키워드
초록
In this paper we study $h$-projectively semisymmetric, φ-pro-jectively semisymmetric, $h$-Weyl semisymmetric and φ-Weyl semisym- metric non-Sasakian ($k$, μ)-contact metric manifolds. In all the cases the manifold becomes an ${\eta}$-Einstein manifold. As a consequence of these results we obtain that if a 3-dimensional non-Sasakian ($k$, μ)-contact metric manifold satisfies such curvature conditions, then the manifold reduces to an N($k$)-contact metric manifold.
Abstract
In this paper we study $h$-projectively semisymmetric, φ-pro-jectively semisymmetric, $h$-Weyl semisymmetric and φ-Weyl semisym- metric non-Sasakian ($k$, μ)-contact metric manifolds. In all the cases the manifold becomes an ${\eta}$-Einstein manifold. As a consequence of these results we obtain that if a 3-dimensional non-Sasakian ($k$, μ)-contact metric manifold satisfies such curvature conditions, then the manifold reduces to an N($k$)-contact metric manifold.
참고문헌 (11)
- D. E. Blair, "Contact metric manifolds satisfying a nullity condition", Israel J. Math, 91(1-3), pp.189~214 (1995)
- E. Boeckx, "A full classification of contact metric $(k,\ mu) $-spaces", Illinois J. Math, 44(1), pp.212~219 (2000)
- E. Boeckx, "ϕ-symmetric contact metric spaces", Glasg. Math. J, 41(3), pp.409~416 (1999)
- U. C. De, "On $\Phi$-recurrent Sasakian manifolds", Novi Sad J. Math, 33(2), pp.43~48 (2003)
- O. Kowalski, "An explicit classi cation of 3-dimensional Riemannian spaces satisfying R(X; Y ) R = 0", Czechoslovak Math. J, 46(3), pp.427~474 (1996)
- B. J. Papantoniou, "Contact Riemannian manifolds satifying R(;X) R = 0 and 2(k; )-nullity distribution", Yokohama Math. J, 40(2), pp.149~161 (1993)
- 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)
- T. Takahashi, "Sasakian ϕ-symmetric spaces", Tohoku Math. J, 29(1), pp.91~113 (1977)
- S. Tanno, "Ricci Curvatures of contact Riemannian manifolds", Tohoku Math. J, 40(3), pp.441~448 (1988)
- J. Vilms, "Submanifolds of Euclidean space with parallel second fundamental form", Proc. Amer. Math. Soc, 32, pp.263~267 (1972)
- K. Yano, "Curvature and Betti numbers, In Annals of Mathematics Studies" (1953), Princeton University Press