Totally real minimal submanifolds in a quaternion projective space

Ximin Liu

Annales Polonici Mathematici (1998)

  • Volume: 69, Issue: 1, page 31-36
  • ISSN: 0066-2216

Abstract

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We prove some pinching theorems with respect to the scalar curvature of 4-dimensional conformally flat (concircularly flat, quasi-conformally flat) totally real minimal submanifolds in QP⁴(c).

How to cite

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Ximin Liu. "Totally real minimal submanifolds in a quaternion projective space." Annales Polonici Mathematici 69.1 (1998): 31-36. <http://eudml.org/doc/270678>.

@article{XiminLiu1998,
abstract = {We prove some pinching theorems with respect to the scalar curvature of 4-dimensional conformally flat (concircularly flat, quasi-conformally flat) totally real minimal submanifolds in QP⁴(c).},
author = {Ximin Liu},
journal = {Annales Polonici Mathematici},
keywords = {totally real submanifold; quaternion projective space; curvature pinching; totally real submanifolds; scalar curvature pinching theorems; quaternionic projective space},
language = {eng},
number = {1},
pages = {31-36},
title = {Totally real minimal submanifolds in a quaternion projective space},
url = {http://eudml.org/doc/270678},
volume = {69},
year = {1998},
}

TY - JOUR
AU - Ximin Liu
TI - Totally real minimal submanifolds in a quaternion projective space
JO - Annales Polonici Mathematici
PY - 1998
VL - 69
IS - 1
SP - 31
EP - 36
AB - We prove some pinching theorems with respect to the scalar curvature of 4-dimensional conformally flat (concircularly flat, quasi-conformally flat) totally real minimal submanifolds in QP⁴(c).
LA - eng
KW - totally real submanifold; quaternion projective space; curvature pinching; totally real submanifolds; scalar curvature pinching theorems; quaternionic projective space
UR - http://eudml.org/doc/270678
ER -

References

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  1. [1] B. Y. Chen and C. S. Houh, Totally real submanifolds of a quaternion projective space, Ann. Mat. Pura Appl. 120 (1979), 185-199. Zbl0413.53031
  2. [2] S. Funabashi, Totally real submanifolds of a quaternionic Kaehlerian manifold, Kodai Math. Sem. Rep. 29 (1978), 261-270. Zbl0391.53025
  3. [3] S. Ishihara, Quaternion Kählerian manifolds, J. Differential Geom. 9 (1974), 483-500. Zbl0297.53014
  4. [4] Y. B. Shen, Totally real minimal submanifolds in a quaternion projective space, Chinese Ann. Math. Ser. B 14 (1993), 297-306. Zbl0811.53061
  5. [5] K. Yano, Concircular geometry I, Proc. Imp. Acad. Sci. Japan Tokyo 16 (1940), 195-200. 
  6. [6] K. Yano and S. Sawaki, Riemannian manifolds admitting a conformal transformation group, J. Differential Geom. 2 (1968), 161-184. Zbl0167.19802

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