• Title, Summary, Keyword: shape operator

Search Result 149, Processing Time 0.046 seconds

Real Hypersurfaces in the Complex Hyperbolic Quadric with Killing Shape Operator

  • Jeong, Imsoon;Suh, Young Jin
    • Kyungpook Mathematical Journal
    • /
    • v.57 no.4
    • /
    • pp.683-699
    • /
    • 2017
  • We introduce the notion of Killing shape operator for real hypersurfaces in the complex hyperbolic quadric $Q^{m*}=SO_{m,2}/SO_mSO_2$. The Killing shape operator implies that the unit normal vector field N becomes A-principal or A-isotropic. Then according to each case, we give a complete classification of real hypersurfaces in $Q^{m*}=SO_{m,2}/SO_mSO_2$ with Killing shape operator.

SHAPE OPERATOR AH FOR SLANT SUBMANIFOLDS IN GENERALIZED COMPLEX SPACE FORMS

  • KIM, DONG-SOO;KIM, YOUNG-HO;LEE, CHUL-WOO
    • Bulletin of the Korean Mathematical Society
    • /
    • v.42 no.1
    • /
    • pp.189-201
    • /
    • 2005
  • In this article, we establish relations between the sectional curvature function K and the shape operator, and also relationship between the k-Ricci curvature and the shape operator for slant submanifolds in generalized complex space forms with arbitrary codimension.

SHAPE OPERATOR OF SLANT SUBMANIFOLDS IN SASAKIAN SPACE FORMS

  • Kim, Young-Ho;Lee, Chul-Woo;Yoon, Dae-Won
    • Bulletin of the Korean Mathematical Society
    • /
    • v.40 no.1
    • /
    • pp.63-76
    • /
    • 2003
  • In this article, we establish relations between the sectional curvature and the shape operator and also between the k-Ricci curvature and the shape operator for a slant submanifold in a Sasakian space form of constant $\varphi-sectional$ curvature with arbitrary codimension.

SOME INEQUALITIES ON TOTALLY REAL SUBMANIFOLDS IN LOCALLY CONFORMAL KAEHLER SPACE FORMS

  • Alfonso, Carriazo;Kim, Young-Ho;Yoon, Dae-Won
    • Journal of the Korean Mathematical Society
    • /
    • v.41 no.5
    • /
    • pp.795-808
    • /
    • 2004
  • In this article, we establish sharp relations between the sectional curvature and the shape operator and also between the k-Ricci curvature and the shape operator for a totally real submanifold in a locally conformal Kaehler space form of constant holomorphic sectional curvature with arbitrary codimension. mean curvature, sectional curvature, shape operator, k-Ricci curvature, locally conformal Kaehler space form, totally real submanifold.

SHAPE OPERATOR AND GAUSS MAP OF POINTWISE 1-TYPE

  • KIM, DONG-SOO;KIM, YOUNG HO
    • Journal of the Korean Mathematical Society
    • /
    • v.52 no.6
    • /
    • pp.1337-1346
    • /
    • 2015
  • We examine the relationship of the shape operator of a surface of Euclidean 3-space with its Gauss map of pointwise 1-type. Surfaces with constant mean curvature and right circular cones with respect to some properties of the shape operator are characterized when their Gauss map is of pointwise 1-type.

REAL HYPERSURFACES OF TYPE A IN COMPLEX TWO-PLANE GRASSMANNIANS RELATED TO THE NORMAL JACOBI OPERATOR

  • Jeong, Im-Soon;Suh, Young-Jin;Tripathi, Mukut Mani
    • Bulletin of the Korean Mathematical Society
    • /
    • v.49 no.2
    • /
    • pp.423-434
    • /
    • 2012
  • In this paper we give a characterization of real hypersurfaces of type (A) in a complex two-plane Grassmannian $G_2(\mathbb{C}^{m+2})$ which is a tube over a totally geodesic $G_2(\mathbb{C}^{m+1})$ in $G_2(\mathbb{C}^{m+2})$, in terms of two commuting conditions related to the normal Jacobi operator and the shape operator.

REAL HYPERSURFACES IN COMPLEX TWO-PLANE GRASSMANNIANS WHOSE SHAPE OPERATOR IS OF CODAZZI TYPE IN GENERALIZED TANAKA-WEBSTER CONNECTION

  • Cho, Kyusuk;Lee, Hyunjin;Pak, Eunmi
    • Bulletin of the Korean Mathematical Society
    • /
    • v.52 no.1
    • /
    • pp.57-68
    • /
    • 2015
  • In this paper, we give a non-existence theorem of Hopf hypersurfaces in complex two-plane Grassmannians $G_2(\mathbb{C}^{m+2})$, $m{\geq}3$, whose shape operator is of Codazzi type in generalized Tanaka-Webster connection $\hat{\nabla}^{(k)}$.

The Shape Operator of the Tubular Hypersurfaces

  • Cho, Bong-Sik
    • Journal for History of Mathematics
    • /
    • v.11 no.1
    • /
    • pp.42-46
    • /
    • 1998
  • Using Fermi coordinates and the principle curvature on the tubula hypersurfaces, we characterize space of constant sectional curvature by analysing the shape operator on the tubular hypersurfaces.

  • PDF

Application of the Projection Operator Technique to the Study of NMR Line Shape and Free Induction Decay Curve (NMR 吸收線 모양과 誘導磁氣自由減衰曲線 硏究에의 投影演算子法의 應用)

  • Lee Jo W.;Sung Nak Jun
    • Journal of the Korean Chemical Society
    • /
    • v.21 no.5
    • /
    • pp.362-371
    • /
    • 1977
  • In this paper application of the projection operator technique to the study of NMR absorption line shape and free induction decay curve is explored. It is found that the projection operator technique can provide a convenient means for deriving a set of hierarchy equations which may serve as a good starting point for theoretical calculation of the absorption line and free induction decay function by successive approximation or by an appropriate decoupling approximation. A brief review of linear response theory of NMR line shape and the relation between the absorption line shape and free induction decay function are also described.

  • PDF