Contact CR-submanifolds with parallel mean curvature vector of a Sasakian space form

U-Hang Ki; Masahiro Kon

Colloquium Mathematicae (1993)

  • Volume: 64, Issue: 2, page 173-184
  • ISSN: 0010-1354

Abstract

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The purpose of this paper is to study contact CR-submanifolds with nonvanishing parallel mean curvature vector immersed in a Sasakian space form. In §1 we state general formulas on contact CR-submanifolds of a Sasakian manifold, especially those of a Sasakian space form. §2 is devoted to the study of contact CR-submanifolds with nonvanishing parallel mean curvature vector and parallel f-structure in the normal bundle immersed in a Sasakian space form. Moreover, we suppose that the second fundamental form of a contact CR-submanifold commutes with the f-structure in the tangent bundle, and compute the restricted Laplacian for the second fundamental form in the direction of the mean curvature vector. As applications of this, in §3, we prove our main theorems.

How to cite

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Ki, U-Hang, and Kon, Masahiro. "Contact CR-submanifolds with parallel mean curvature vector of a Sasakian space form." Colloquium Mathematicae 64.2 (1993): 173-184. <http://eudml.org/doc/210182>.

@article{Ki1993,
abstract = {The purpose of this paper is to study contact CR-submanifolds with nonvanishing parallel mean curvature vector immersed in a Sasakian space form. In §1 we state general formulas on contact CR-submanifolds of a Sasakian manifold, especially those of a Sasakian space form. §2 is devoted to the study of contact CR-submanifolds with nonvanishing parallel mean curvature vector and parallel f-structure in the normal bundle immersed in a Sasakian space form. Moreover, we suppose that the second fundamental form of a contact CR-submanifold commutes with the f-structure in the tangent bundle, and compute the restricted Laplacian for the second fundamental form in the direction of the mean curvature vector. As applications of this, in §3, we prove our main theorems.},
author = {Ki, U-Hang, Kon, Masahiro},
journal = {Colloquium Mathematicae},
keywords = {contact CR-manifolds},
language = {eng},
number = {2},
pages = {173-184},
title = {Contact CR-submanifolds with parallel mean curvature vector of a Sasakian space form},
url = {http://eudml.org/doc/210182},
volume = {64},
year = {1993},
}

TY - JOUR
AU - Ki, U-Hang
AU - Kon, Masahiro
TI - Contact CR-submanifolds with parallel mean curvature vector of a Sasakian space form
JO - Colloquium Mathematicae
PY - 1993
VL - 64
IS - 2
SP - 173
EP - 184
AB - The purpose of this paper is to study contact CR-submanifolds with nonvanishing parallel mean curvature vector immersed in a Sasakian space form. In §1 we state general formulas on contact CR-submanifolds of a Sasakian manifold, especially those of a Sasakian space form. §2 is devoted to the study of contact CR-submanifolds with nonvanishing parallel mean curvature vector and parallel f-structure in the normal bundle immersed in a Sasakian space form. Moreover, we suppose that the second fundamental form of a contact CR-submanifold commutes with the f-structure in the tangent bundle, and compute the restricted Laplacian for the second fundamental form in the direction of the mean curvature vector. As applications of this, in §3, we prove our main theorems.
LA - eng
KW - contact CR-manifolds
UR - http://eudml.org/doc/210182
ER -

References

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  1. [1] U-H. Ki, M. Kameda and S. Yamaguchi, Compact totally real submanifolds with parallel mean curvature vector field in a Sasakian space form, TRU Math. 23 (1987), 1-15. Zbl0701.53074
  2. [2] U-H. Ki and J. S. Pak, On totally real submanifolds with parallel mean curvature vector of a Sasakian space form, Bull. Korean Math. Soc. 28 (1991), 55-64. Zbl0727.53058
  3. [3] E. Pak, U-H. Ki, J. S. Pak and Y. H. Kim, Generic submanifolds with normal f-structure of an odd-dimensional sphere (I), J. Korean Math. Soc. 20 (1983), 141-161. Zbl0535.53043
  4. [4] K. Yano, On a structure defined by a tensor field f of type (1,1) satisfying f 3 + f = 0 , Tensor (N.S.) 14 (1963), 99-109. Zbl0122.40705
  5. [5] K. Yano and M. Kon, Generic submanifolds of Sasakian manifolds, Kodai Math. J. 3 (1980), 163-196. Zbl0452.53034
  6. [6] K. Yano and M. Kon, CR Submanifolds of Kaehlerian and Sasakian Manifolds, Birkhäuser, Boston 1983. Zbl0496.53037
  7. [7] K. Yano and M. Kon, Structures on Manifolds, World Sci., 1984. 
  8. [8] K. Yano and M. Kon, On contact CR submanifolds, J. Korean Math. Soc. 26 (1989), 231-262. Zbl0694.53050

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