# RICCI CURVATURE OF SUBMANIFOLDS IN A QUATERNION PROJECTIVE SPACE

• Liu, Ximin (Department of Mathematics, Rutgers University) ;
• Dai, Wanji (Department of Applied Mathematics, Dalian University of Technology)
• 발행 : 2002.10.01

#### 초록

Recently, Chen establishes sharp relationship between the k-Ricci curvature and the squared mean curvature for a submanifold in a Riemannian space form with arbitrary codimension. In this paper, we establish sharp relationships between the Ricci curvature and the squared mean curvature for submanifolds in quaternion projective spaces.

#### 참고문헌

1. Proc. Royal Soc. Edinburgh, Sect. A, Math v.126 An exotic totally real minimal immersion of S³ and CP³ and its charac-terization https://doi.org/10.1017/S0308210500030651
2. Arch. Math v.63 Totally real submanifolds of C Pn satisfying a basic equality B.Y. Chen;F. Dillen;L. Verstraelen;L. Vrancken https://doi.org/10.1007/BF01202073
3. J. Diff. Geom v.9 Quaternion Kaehoerian manifolds S. Ishihara https://doi.org/10.4310/jdg/1214432544
4. Glasgow Math J. v.41 Relations between Ricci curvature and shape operator for submanifolds with arbitrary codimension https://doi.org/10.1017/S0017089599970271
5. Ann. Mat. Pura Appl v.120 Totally real submanifolds of a quaternion projective space B.Y. Chen;C.S. Houh https://doi.org/10.1007/BF02411943
6. Arch. Math v.60 Some pinching and classification theorems for minimal submanifolds B.Y. Chen https://doi.org/10.1007/BF01236084
7. Glasgow Math J. v.38 Mean curvature and shape operator of isometric immersions in real space form https://doi.org/10.1017/S001708950003130X

#### 피인용 문헌

1. On Chen invariants and inequalities in quaternionic geometry vol.2013, pp.1, 2013, https://doi.org/10.1186/1029-242X-2013-66