• 제목/요약/키워드: Sasakian

검색결과 177건 처리시간 0.023초

A NEW TYPE WARPED PRODUCT METRIC IN CONTACT GEOMETRY

  • Mollaogullari, Ahmet;Camci, Cetin
    • 호남수학학술지
    • /
    • 제44권1호
    • /
    • pp.62-77
    • /
    • 2022
  • This study presents an 𝛼-Sasakian structure on the product manifold M1 × 𝛽(I), where M1 is a Kähler manifold with an exact 1-form, and 𝛽(I) is an open curve. It then defines a new type warped product metric to study the warped product of almost Hermitian manifolds with almost contact metric manifolds, contact metric manifolds, and K-contact manifolds.

RICCI CURVATURE OF INTEGRAL SUBMANIFOLDS OF AN S-SPACE FORM

  • Kim, Jeong-Sik;Dwivedi, Mohit Kumar;Tripathi, Mukut Mani
    • 대한수학회보
    • /
    • 제44권3호
    • /
    • pp.395-406
    • /
    • 2007
  • Involving the Ricci curvature and the squared mean curvature, we obtain a basic inequality for an integral submanifold of an S-space form. By polarization, we get a basic inequality for Ricci tensor also. Equality cases are also discussed. By giving a very simple proof we show that if an integral submanifold of maximum dimension of an S-space form satisfies the equality case, then it must be minimal. These results are applied to get corresponding results for C-totally real submanifolds of a Sasakian space form and for totally real submanifolds of a complex space form.

SCALAR CURVATURE OF CONTACT THREE CR-SUBMANIFOLDS IN A UNIT (4m + 3)-SPHERE

  • Kim, Hyang-Sook;Pak, Jin-Suk
    • 대한수학회보
    • /
    • 제48권3호
    • /
    • pp.585-600
    • /
    • 2011
  • In this paper we derive an integral formula on an (n + 3)-dimensional, compact, minimal contact three CR-submanifold M of (p-1) contact three CR-dimension immersed in a unit (4m+3)-sphere $S^{4m+3}$. Using this integral formula, we give a sufficient condition concerning the scalar curvature of M in order that such a submanifold M is to be a generalized Clifford torus.

THE k-ALMOST RICCI SOLITONS AND CONTACT GEOMETRY

  • Ghosh, Amalendu;Patra, Dhriti Sundar
    • 대한수학회지
    • /
    • 제55권1호
    • /
    • pp.161-174
    • /
    • 2018
  • The aim of this article is to study the k-almost Ricci soliton and k-almost gradient Ricci soliton on contact metric manifold. First, we prove that if a compact K-contact metric is a k-almost gradient Ricci soliton, then it is isometric to a unit sphere $S^{2n+1}$. Next, we extend this result on a compact k-almost Ricci soliton when the flow vector field X is contact. Finally, we study some special types of k-almost Ricci solitons where the potential vector field X is point wise collinear with the Reeb vector field ${\xi}$ of the contact metric structure.

SECTIONAL CURVATURE OF CONTACT C R-SUBMANIFOLDS OF AN ODD-DIMENSIONAL UNIT SPHERE

  • Kim, Hyang-Sook;Pak, Jin-Suk
    • 대한수학회보
    • /
    • 제42권4호
    • /
    • pp.777-787
    • /
    • 2005
  • In this paper we study (n + 1)-dimensional compact contact CR-submanifolds of (n - 1) contact CR-dimension immersed in an odd-dimensional unit sphere $S^{2m+1}$. Especially we provide necessary conditions in order for such a sub manifold to be the generalized Clifford surface $$S^{2n_1+1}(((2n_1+1)/(n+1))^{\frac{1}{2}})\;{\times}\;S^{2n_2+1}(((2n_2+1)/(n+1)^{\frac{1}{2}})$$ for some portion (n1, n2) of (n - 1)/2 in terms with sectional curvature.

ON 3-DIMENSIONAL NORMAL ALMOST CONTACT METRIC MANIFOLDS SATISFYING CERTAIN CURVATURE CONDITIONS

  • De, Uday Chand;Mondal, Abul Kalam
    • 대한수학회논문집
    • /
    • 제24권2호
    • /
    • pp.265-275
    • /
    • 2009
  • The object of the present paper is to study 3-dimensional normal almost contact metric manifolds satisfying certain curvature conditions. Among others it is proved that a parallel symmetric (0, 2) tensor field in a 3-dimensional non-cosympletic normal almost contact metric manifold is a constant multiple of the associated metric tensor and there does not exist a non-zero parallel 2-form. Also we obtain some equivalent conditions on a 3-dimensional normal almost contact metric manifold and we prove that if a 3-dimensional normal almost contact metric manifold which is not a ${\beta}$-Sasakian manifold satisfies cyclic parallel Ricci tensor, then the manifold is a manifold of constant curvature. Finally we prove the existence of such a manifold by a concrete example.