Portugaliae Mathematica   EMIS ELibM Electronic Journals PORTUGALIAE
Vol. 58, No. 2, pp. 219-231 (2001)

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On Totally Real Submanifolds in A Nearly Kähler Manifold

Zhong Hua Hou

Department of Applied Mathematics, Dalian University of Technology,
Dalian 116024, Liaoning -- PEOPLE'S REPUBLIC OF CHINA
E-mail: zhhou@dlut.edu.cn
CMAF, Universidade de Lisboa,
Av. Prof. Gama Pinto, 2, 1649-003 Lisboa -- PORTUGAL
E-mail: zhhou@lmc.fc.ul.pt

Abstract: Let $M^m$ be a totally real submanifold of a nearly Kähler manifold $\bar M^{2m}$. We prove an important relationship between the covariant differential of the second fundamental form of $M^m$ and that of the almost complex structure of $\bar M^{2m}$. And we show an application to the pinching problem on the square of the length of the second fundamental form of $M^m$.

Keywords: Nearly Kähler manifold; Totally real submanifold.

Classification (MSC2000): 53C42.; 32v40.

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Electronic version published on: 9 Feb 2006. This page was last modified: 27 Nov 2007.

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